Mdtop March 2015

mdtop@mathdept.okstate.edu

2 participants
4 discussions

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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Mdtop March 2015