## Strenner: Pseudo-Anosov mapping classes not arising from Penner’s construction

Balazs Strenner, a Ph.D. student of Richard Kent graduating this year, gave a beautiful talk yesterday in our geometry/topology seminar about his recent paper with Hyunshik Shin.  (He’s at the Institute next year but if you’re looking for a postdoc after that…!)

A long time ago, Robert Penner showed how to produce a whole semigroup M in the mapping class group with the property that all but a specified finite list of elements of M were pseudo-Anosov.  So that’s a good cheap way to generate lots of certified pseudo-Anosovs in the mapping class group.  But of course one asks:  do you get all pA’s as part of some Penner semigroup?  This can’t quite be true, because it turns out that the Penner elements can’t permute singularities of the invariant folation, while arbitrary pA’s can.  But there are only finitely many singularities, so some power of a given pA clearly fixes the singularities.

So does every pA have a power that arises from Penner’s construction?  This is what’s known as Penner’s conjecture.  Or was, because Balazs and Hyunshik have shown that it is falsitty false false false.

When I heard the statement I assumed this was going to be some kind of nonconstructive counting argument — but no, they actually give a way of proving explicitly that a given pA is not in a Penner semigroup.  Here’s how.  Penner’s semigroup M is generated by Dehn twists Q_1, … Q_m, which all happen to preserve a common traintrack, so that there’s actually a representation

$\rho: M \rightarrow GL_n(\mathbf{R})$

such that the dilatation of g is the Perron-Frobenius eigenvalue $\lambda$ of $\rho(g)$.

Now here’s the key observation; there is a quadratic form F on R^n such that F(Q_i x) >= F(x) for all x, with equality only when x is a fixed point of Q_i.  In particular, this shows that if g is an element of M not of the form Q_i^a, and x is an arbitrary vector, then the sequence

$x, g x, g^2 x, \ldots$

can’t have a subsequence converging to x, since

$F(x), F(gx), F(g^2 x), \ldots$

is monotone increasing and thus can’t have a subsequence converging to F(x).

This implies in particular:

g cannot have any eigenvalues on the unit circle.

But now we win!  Because $\rho(g)$ is an integral matrix, so all the Galois conjugates of $\lambda$ must be among its eigenvalues.  In other words, $\lambda$ is an algebraic number none of whose Galois conjugates lie on the unit circle.  But there are lots of pseudo-Anosovs whose dilatations $\lambda$ do have Galois conjugates on the unit circle.  In fact, experiments by Dunfield and Tiozzo seem to show that in a random walk on the braid group, the vast majority of pAs have this property!  And these pAs, which Shin and Strenner call coronal, cannot appear in any Penner semigroup.

Cool!

Anyway, I found the underlying real linear algebra question very appealing.  Two idle questions:

• If M is a submonoid of GL_n(R) we may say a continuous real-valued function F on R^n is M-monotone if F(mx) >= F(x) for all m in M, x in R^n.  The existence of a monotone function for the Penner monoid is the key to Strenner and Shin’s theorem.  But I have little feeling for how it works in general.  Given a finite set of matrices, what are explicit conditions that guarantee the existence of an M-monotone function?  Nonexistence?  (I have a feeling it is roughly equivalent to M containing no element with an eigenvalue on the unit circle, but I’m not sure, and anyway, this is not a checkable condition on the generating matrices…)
• What can we say about the eigenvalues of matrices appearing in the Penner subgroup?  Balazs says he’ll show in a later paper that they can actually get arbitrarily close to the unit circle, which is actually not what I had expected.  He asks:  are those eigenvalues actually dense in the complex plane?

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## ageofdestruction: solar corona, photographed by stereo a, 8th…

solar corona, photographed by stereo a, 8th september 2012.

20 images over 10 hours, inverted. the dots moving in the background are stars.

image credit: nasa/stereo. animation: ageofdestruction.

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## myjetpack: My book of cartoons ‘You’re All Just Jealous of my…

My book of cartoons ‘You’re All Just Jealous of my Jetpack’ is available now:US: http://www.amazon.com/dp/1770461043
UK: http://www.amazon.co.uk/dp/1770461043
Other stockists, info and prints for sale at www.tomgauld.com

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## Code-X (49)

Explosive Potential
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## uneven-growth: A promise is a cloud (2014) appropriates…

A promise is a cloud (2014) appropriates artisanal techniques used to harvest water from fog. The nets provide daily up to 1,000 litres of water for a community of 500 families in the outskirts of Lima, who like millions of Limeños live without access to clean water.

Inspired by an Arab saying, the project presents a critical reflection of Lima based on its meteorological conditions: a city spread throughout the desert, whose main source of water comes from melting glaciers and is permanently covered by a gloomy cloud that rarely produces any rain.

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## “On Tuesday, I attended court for the Silk Road trial closing arguments and watched the defense…”

“On Tuesday, I attended court for the Silk Road trial closing arguments and watched the defense struggle to carve out a plausible defense of their client. All of the blended fiction and real elements of life on the internet were yanked from the dark mirror and presented as evidence to a courtroom full of people who left their digital devices with security at check through. It is entirely reasonable to believe Ross Ulbricht was a pretty nice, normal seeming guy and also Dread Pirate Roberts, the Silk Road kingpin. That’s not to say he got carried away either. Silk Road was an ideological anarcho-capitalist enterprise. (One of the exhibits, notes on daily operation of the deep web black market included this handshake: “read any good books lately?” “anything by rothbard.”)”

-

The Internet is Real — The Message — Medium

I wrote this ;)

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## groundhog bites mayor

groundhog bites mayor

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## Bob Marley

“Babylon system is the vampire”
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## noseracontacto: A girl smeared with colors reacts as another…

A girl smeared with colors reacts as another girl throws powder at her during Holi celebrations in Chennai on March 16, 2014.(Reuters/Babu)

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clown

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## “Within the next generation I believe that the world’s rulers will discover that infant…”

“Within the next generation I believe that the world’s rulers will discover that infant conditioning and narco-hypnosis are more efficient, as instruments of government, than clubs and prisons, and that the lust for power can be just as completely satisfied by suggesting people into loving their servitude as by flogging and kicking them into obedience. In other words, I feel that the nightmare of Nineteen Eighty-Four is destined to modulate into the nightmare of a world having more resemblance to that which I imagined in Brave New World. The change will be brought about as a result of a felt need for increased efficiency. Meanwhile, of course, there may be a large scale biological and atomic war — in which case we shall have nightmares of other and scarcely imaginable kinds.”

- Letters of Note: 1984 v. Brave New World
Aldous Huxley in a letter to George Orwell
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## thingsmagazine: Cardboard City: Brutal London

Cardboard City: Brutal London

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## brownshoesonly: standard patching #CRTpic

standard patching #CRTpic

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The Decision
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## kiameku: Magnus Thierfelder Fountain 2004 Coleman Project,…

Magnus Thierfelder
Fountain
2004
Coleman Project, London

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## coitusandcarnage: publicity photo by Helmut Newton for Bram…

publicity photo by Helmut Newton for Bram Stoker’s Dracula

Vanity Fair, 1992

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## Air Bridge (1)

I pushed the paper away and said, "Why didn’t you hand me over?"
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## How to hold a blood drive in the spirit of intellectual freedom

It’s been fun being able to follow along with the ALA Midwinter conference on a bunch of different social media fronts. I was just reading the Stonewall Book Awards press release (congrats everyone) and noticed the GLBT Round Table page where I read the press release about the blood drive that happened during ALA. And it made me happy. Both because there was a blood drive but also because there was the recognition of the discriminatory nature of the decisions regarding the eligible donor pool–nearly all gay and bisexual men can’t donate blood at all–and they not only mention this in the press release but there is a panel discussing this and related issues. Nice work.

ALA and LBC (Librarians Build Communities) recognize there are many restrictions regarding blood donations. Among those is the ban on accepting blood donations from men who have had sex with another man since 1977. This effectively removes all gay and bisexual men from being eligible blood donors. However, the FDA has recently announced plans to relax the ban to allow donations by gay and bisexual men if they have not had sex with another man in the past year.

From the onset, this ban has been controversial. While the government has imposed exclusions that limit or restrict the donor pool, the ban on accepting blood donations from gay and bisexual men is deemed by many as unjustified and discriminatory, unfairly prohibiting healthy men from donating much needed, life-saving blood.

In an effort to educate the library community about the issues regarding blood donations, the ALA Gay, Lesbian, Bisexual, and Transgender Round Table (GLBTRT) is sponsoring the discussion panel “Blood Donation: Facts, Fear, and Discrimination,” on Sunday, Feb. 1, 2015, from 8:30 a.m. to 10 a.m. LBC supports the GLBTRT’s panel discussion and encourages ALA members to both donate blood and attend the panel discussion to be informed and have their voices heard.

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But even if Hyundai is eventually forced to pay the full amount of the damages, the punishment could be substantially reduced through a tax loophole that permits the company to save millions of dollars by deducting any court-ordered punitive damages as an ordinary business expense. The result, critics say, is that taxpayers are in effect subsidizing corporate misconduct.

What’s terrible about this isn’t that companies are allowed to claim the fines they pay for malfeasance are an ordinary business expense.  What’s terrible is that it’s true.

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## icancauseaconstellation: Michel Rougier… Saul Steinberg at work…

Michel Rougier… Saul Steinberg at work on humorous cutouts depicting “People of America” at Brussels World’s Fair 1958 @ life

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## narcissistic—panda:don’t mind the dancing groot. :)

don’t mind the dancing groot. :)

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Ironic Biker
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## fabriciusitalicus:Alois Kolb (1875-1942), ex-libris

Alois Kolb (1875-1942), ex-libris

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## postgraduategoth:vintagebrides:1935, Cleveland, Ohio – Minnie…

1935, Cleveland, Ohio - Minnie Ruth Solomon waiting at the train station for her fiance, Olympic champion Jesse Owens on the eve of their wedding.

Gorgeous.

I’d totally wear that!

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## One of the best-loved places to eat is Watts Coffee House, the…

One of the best-loved places to eat is Watts Coffee House, the roots of which lie in the Watts Happening Coffee House, which opened shortly after the rebellion. Bruce and I first walked right past the restaurant because it’s practically hidden inside a building shared with a school. We did notice the mural, which is a holdover from the building’s past as the home of the Mafundi Institute in the early 1970s.

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## “Cyberspies used social engineering trickery to steal Syrian opposition’s strategies and battle…”

“Cyberspies used social engineering trickery to steal Syrian opposition’s strategies and battle plans, according to security researchers. Hackers employed a familiar tactic: ensnaring victims through conversations with seemingly sympathetic and attractive women. As the conversations progressed onto Skype chats, the “women” would offer up a personal photo that was laden with malware and designed to compromise the target’s computer or Android phone.”

-

Fake hottie hackers flung info-slurping malware at Syrian opposition – FireEye • The Register

via melissa

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## evergod:The Flight of Moloch, 1809 William Blake

The Flight of Moloch, 1809

William Blake

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## gifopera: temple of the running man(a slight variation of this…

temple of the running man

(a slight variation of this gif)

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## The High Wire (14)

‘I’m a man without honour but I’m not a dishonoured man.’
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## nitratediva: Harold Lloyd in The Freshman (1925).

Harold Lloyd in The Freshman (1925).

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## “What started with dozens of re-purposed boy scouts grew to hundreds, but there it hit a ceiling….”

What started with dozens of re-purposed boy scouts grew to hundreds, but there it hit a ceiling. When that happened, Putin’s team approached Russian advertisers. According to my sources, there are currently 10 different advertising agencies working for the Kremlin. These contracts are secret, and the firms are careful to maintain other, non-political clients.

The agencies compete fiercely with one another for contract extensions and bigger deals, making Russia’s online propaganda industry quite lucrative and surprisingly effective. It’s like Adam Smith’s “invisible hand,” except the opposite.

Combined, these efforts field a troll army of thousands. In some areas, like on the outskirts of St. Petersburg, the enterprise is so big that there are whole office buildings for these people.

It seems like a joke, but thousands of hired bloggers “go to work” every day, writing online about Vladimir Putin’s greatness and the decay of the West. They’re on Facebook, Twitter, news sites, and anywhere else the Kremlin feels threatened and outnumbered. Fresh instructions arrive every day in emails, specifying what to say and where to post it, all with the aim of bolstering Putin’s presidency amidst war and economic crisis.

- How Putin Secretly Conquered Russia’s Social Media Over the Past 3 Years · Global Voices
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# ROBERT GREENE discusses his and Catherine Texier's translation of JACQUES MESRINE'S THE DEATH INSTINCT

The Death Instinct (Tam Tam Books)
France's Public Enemy Number One from the late 1960s to the end of the 1970s--when he was killed by police in a sensational traffic shootout--Jacques Mesrine (1936-1979) is the best-known criminal in French history. Mesrine was notorious both for his violent exploits and for the media attention he attracted, and he remains very much a public media figure in France and Europe. In 2008 there were two feature-length films based on his life, one of them starring Vincent Cassel in the lead role. Mesrine wrote The Death Instinct while serving time in the high-security prison La Sante; the manuscript was smuggled out of the prison and was later published by Guy Debord's publisher Gerard Lebovici (who briefly adopted Mesrine's daughter, Sabrina, before being assassinated, a few years after Mesrine). The Death Instinct deals with the early years of Mesrine's criminal life, including a horrifically graphic description of a murder he committed early on in his career and a highly detailed account of the workings of the French criminal underworld--making this book perhaps one of the most intriguing and detailed anthropological studies of a criminal culture ever written.
Praise for The Death Instinct:
"Jacques Mesrine was a modern Robin Hood. Modern in the sense that his story includes violence, spectacle, and that he is not just a figure of legend. He did not let the tabloids write the only version of the story. He wrote this remarkable book. About the only thing Guy Debord and Michel Foucault ever agreed on is that this book is a top read." --McKenzie Wark, author of The Beach Beneath the Street
"Unputdownable, incendiary real-life noir. With a touch of Belle-Epoque anarchist criminal Bonnot, nurtured by disposition, pathology and war. No wonder Situationists admired this escape-artist-sociopath, whose sense of honor and justice was matched only by his contempt for society. In literate and lucid contraband prison prose which, as Mesrine says, mixes all the genres: “burlesque, gore, violence, friendship, and fugitives on the lam.” Too bad this "man of a thousand faces" isn't around to help deal with present-day bank corruption, or, for that matter, the prison-industrial complex."--Woody Haut, author of Heartbreak and Vine and Pulp Culture: Hardboiled Fiction and the Cold War
Robert Greene is the author of five books: The 48 Laws of Power (Penguin), The Art of Seduction (Penguin), The Strategies of War, (Penguin) The 50th Law (co-written with the rapper 50 cent, Harper Books), and Mastery (Penguin)He is currently at work on his next book, The Laws of Human Nature (Penguin). He has previously translated from the French, Considerations on the Assassination of Gérard Lebovici, Guy Debord (Tam Tam books). Robert Greene lives in Los Feliz.
Robert Greene photo by Susan Anderson
Event date:
Thursday, February 12, 2015 - 7:30pm
1818 N Vermont Ave
Los AngelesCA 90027

## The Death Instinct (Paperback)

By Jacques MesrineRobert Greene (Translator), Catherine Texier (Translator)

His oldest son, Daniel, who was 15 at the time, remembers the moment his father walked into the house and dumped the $10,000 or so on a table. “It looked like he had robbed a bank,” he said. Parker was trying to teach his kids a lesson about the value of money. But the lesson I would learn from this is “If somebody, like a bank teller, works in a service job, and makes a lot less money than I do, I can make them spend a full day of their life carrying out an incredibly tedious task without thinking about whether this is a reasonable way for them to spend their time.” Uncategorized ## John Ford Entertainment, grand landscapes, and dialectical troubles. Uncategorized ## S.J. Perelman Strutting, superior but somehow also self- deprecating. Uncategorized ## Full professors make more money than bus drivers Former Republican Congressional candidate and current UW-Madison history professor John Sharpless stands up for us against the Governor: He said he arrives no later than 9 a.m. and leaves no earlier than 5 p.m. During that time, he said he’s either teaching, preparing lectures, doing research, attending required committee meetings, advising students and managing teaching assistants. Sharpless added that he often spends his evenings reading and grading papers. “None of this seems like work to a guy like Walker because he lives a different life,” he said. “And I’m not going to make fun of what he does. I’m sure being a governor is a lot of work. He has to spend a lot of time in Iowa and South Carolina and North Carolina and courting other Republican big-wigs. That taxes the man horribly.” But just to make it clear he’s still on board with GOP, he drops this in: “I will retire with a salary that’s less than a Madison bus driver,” he said. UW-Madison salaries are public records, so I can tell you that Sharpless’s is just under$80,000.  In 2012, only 9 employees of Metro made more than \$70K.  And the ones who made that much, I’m pretty sure, are the ones who worked tons of overtime.

In other words, what Sharpless said is likely true in the strict sense of

“There exists a Madison bus driver whose salary this year exceeds mine”

but gives the wrong impression about typical full professors in the history department and typical bus drivers.

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