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Seminar time change
by Henry Segerman 08 Apr '15

08 Apr '15

Pengcheng Xu's talk will now be next week, April 16th, 3:30pm MSCS 514.

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Reminder: Ken Baker speaking today, MSCS 514 at 4pm
by Henry Segerman 06 Apr '15

06 Apr '15

Title: Unifying unexpected exceptional Dehn surgeries Abstract: In summer 2014, Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census. Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.

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Many topology talks
by Henry Segerman 30 Mar '15

30 Mar '15

Hi all, We have many topology talks coming up in the next week. In addition to the Redbud conference over the weekend, Jeff Meier will speak in the usual Thursday 3:30pm timeslot, and Ken Baker will speak at 4:00pm next Monday. Both talks will be in MSCS 514. Titles and abstracts below. Jeff Meier: Bridge trisections for knotted surfaces in $S^4$ Recently, Gay and Kirby introduced a new way of describing a 4--manifold called a \emph{trisection}, which involves decomposing the 4--manifold into three 4--dimensional handlebodies and serves as a 4--dimensional analogue to a Heegaard splitting of a 3--manifold. We adapt their approach to the setting of knotted surfaces in $S^4$; namely, we show that every such surface $\mathcal K$ admits a \emph{bridge trisection}, which is a decomposition of $(S^4,\mathcal K)$ into three pieces, each of which is a collection of trivial disks in $B^4$. A bridge trisection associates two complexity parameters to $\mathcal K$, giving a complexity measure analogous to the bridge number of a classical knot, and we give a classification of knotted surfaces with low bridge number. The theory gives rise to a new way to describe knotted surfaces in $S^4$ diagrammatically in terms of a triple of trivial (classical) tangle diagrams called a \emph{tri-plane diagram}. This is joint work with Alexander Zupan. Ken baker: Unifying unexpected exceptional Dehn surgeries In summer 2014, Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census. Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.

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Spring 2015 Redbud conference
by Henry Segerman 25 Mar '15

25 Mar '15

Hi all, If you plan to attend the Spring Redbud conference (April 3-5, OSU) but have not yet registered, please do so as soon as possible at: http://math.okstate.edu/redbud/ so that we have an accurate headcount. Please forward this on to any others who may also be planning to attend but have not yet registered. Thanks, Henry Segerman

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Nel Abdiel visiting
by Henry Segerman 22 Mar '15

22 Mar '15

Nel Abdiel will be visiting from the University of Iowa next week, arriving Tuesday evening, leaving Friday morning, and speaking in the seminar 3:30pm on Thursday. Title/abstract TBA. Let me or Trent know if you'd like to go to lunch with us on Wednesday or Thursday, or meet with Nel etc. Henry

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Topology seminar
by Henry Segerman 10 Mar '15

10 Mar '15

I will speak in the topology seminar, 3:30pm Thursday, in 514. Title: Veering Dehn surgery Abstract: This is joint work with Saul Schleimer. Veering structures on ideal triangulations of cusped manifolds were introduced by Ian Agol, who showed that every pseudo-Anosov mapping torus over a surface, drilled along all singular points of the measured foliations, has an ideal triangulation with a veering structure. Any such structure coming from Agol's construction is necessarily layered, although a few non-layered structures have been found by randomised search. We introduce veering Dehn surgery, which can be applied to certain veering triangulations, to produce veering triangulations of a surgered manifold. As an application we find an infinite family of transverse veering triangulations none of which are layered. Until recently, it was hoped that veering triangulations might be geometric, however the first counterexamples were found recently by Issa, Hodgson and me. We also apply our surgery construction to find a different infinite family of transverse veering triangulations, none of which are geometric.

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Tian Yang visiting
by Henry Segerman 26 Feb '15

26 Feb '15

Tian Yang will be visiting from Stanford to give the topology seminar next Thursday (Feb 26), and will be around all day Thursday. Let me know if you'd like to go to lunch with us that day, or meet with Tian etc. Here are Tian's talk title and abstract: *On type-preserving representations of the four-punctured sphere group* *Abstract:* We give counterexamples to a conjecture of Bowditch that if a non-elementary type-preserving representation ρ : π1(Σg,n) → PSL(2; R) of a punctured surface group sends every non-peripheral simple closed curve to a hyperbolic element, then ρ must be Fuchsian. The counterexamples come from relative Euler class +/-1 representations of the four-punctured sphere group. As a related result, we show that the mapping class group action on each non-extremal component of the character space of type-preserving representations of the four-punctured sphere group is ergodic. The main tool we use is Penner's lengths coordinates of the decorated character spaces defined by Kashaev. Henry

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Spring 2015 Redbud Geometry / Topology Conference
by Henry Segerman 03 Feb '15

03 Feb '15

Hi all, The Redbud conference website is up now, with details on travel and accommodation, at http://math.okstate.edu/redbud. Please spread the word and register if you plan on attending. Thanks, Sean Bowman Danielle O'Donnol Henry Segerman

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Topology seminar
by Henry Segerman 28 Jan '15

28 Jan '15

Trent Schirmer will speak tomorrow, Thur Jan 29, on: GK-Trisections of 4-manifolds and the Poincare Conjecture Abstract: A GK-trisection of a 4-manifold X is a decomposition of X into three simple handlebodies that intersect in a nice way. Introduced by Gay and Kirby, this construction bears many similarities to Heegaard splittings of 3-manifolds, and is amenable to study using 3-manifold techniques, as is well illustrated in a recent paper by Meier and Zupan. In my talk I will describe how GK-trisections provide new approaches to the 4-dimensional smooth Poincare Conjecture. These approaches are essentially the analogues of failed "Heegaard splitting" approaches to the 3-dimensional Poincare Conjecture. However, the fact that the 3d Poincare conjecture is true implies several statements about or related to Heegaard splittings that maybe, just maybe, can somehow be lifted to statements about trisections that imply the 4-d conjecture.

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Spring 2015 Redbud Geometry / Topology Conference
by Henry Segerman 25 Jan '15

25 Jan '15

First Announcement Spring 2015 Redbud Geometry / Topology Conference WHEN: April 3-5, 2015 WHERE: Oklahoma State University SPEAKERS: Ken Baker, University of Miami John Etnyre, Georgia Tech Dave Futer, Temple University Matt Hedden, Michigan State University Efstratia Kalfagianni, Michigan State University Emmy Murphy, MIT Sinem Onaran, Hacettepe University Jessica Purcell, Brigham Young University Laura Starkston, University of Texas, Austin Andy Wand, University of Nantes The Spring 2015 Redbud conference will be held at Oklahoma State University April 3–5, 2015. The Redbud conference is a regional conference in topology and geometry with participants from the University of Oklahoma, Oklahoma State University, the University of Arkansas, and elsewhere. Friday 3rd of April will be a graduate student workshop, with introductory talks on contact topology and hyperbolic geometry. The main conference will be held on Saturday 4th and Sunday 5th of April. We anticipate funding that will allow us to cover a portion of the travel expenses for participants without other means of support. Graduate student, recent Ph.D.s, and mathematicians in underrepresented groups working in geometric topology are especially encouraged to apply for funding. The conference website is http://math.okstate.edu/redbud We hope to see you in April! Local organizers: Sean Bowman Danielle O'Donnol Henry Segerman

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