Hello everyone,

We have two events going on this week.

Eric Chesebro, Farey recursion and 2-bridge link complements, MSCS 509, Tuesday 3:30pm

Birch Bryant, Fibers as normal and spun-normal surfaces in link manifolds, MSCS 101, Wednesday 3:30pm

For those scattered far and wide, both speakers have given permission to stream there talks. Join Zoom Meeting https://okstate-edu.zoom.us/j/91286033884?pwd=bm9DSGJCbjlldmxHYlh3eDM1cUtwZz...

Meeting ID: 912 8603 3884 Passcode: JSJDecomp One tap mobile +13462487799,,91286033884#,,,,*101999162# US (Houston) +16694449171,,91286033884#,,,,*101999162# US

Here are the abstracts:

Farey recursion and 2-bridge link complements. Speaker: Eric Chesebro, University of Montana Date: Apr 18, 2023 Time: 3:30 PM Room: MSCS 509 Abstract: I will define Farey recursion and explain how it helps us understand the geometries of hyperbolic 2-bridge link complements.

Fibers as normal and spun-normal surfaces in link manifolds Speaker: Birch Bryant, Oklahoma State University Date: Apr 19, 2023 Time: 3:30 PM Room: MSCS 101

Abstract: The theory of Normal Surfaces was developed by Kneser and expanded by Haken to find properly embedded essential surfaces triangulations of compact 3-manifolds. For ideal triangulations of cusped finite-volume hyperbolic 3-manifolds, Walsh showed if the ideal triangulation has essential edges, any incompressible surface $S$ can be realized as a spun-normal surface, provided $S$ is not a virtual fiber. One comes to the natural question posed directly by Cooper, Tillmann, and Worden: "For a fibered knot complement or fibered once-cusped 3-manifold $M$, is there always some ideal triangulation of $M$ such that the fiber is realized as an embedded spun-normal surface?" Using the techniques of crushing and inflating ideal triangulations developed by Jaco and Rubinstein, we will answer this question by giving an algorithm to construct for a fibered knot complement an ideal triangulation, $\mathcal T^*$, in which a fiber of the bundle structure spun-normalizes. The algorithm presented will also identify the fiber within a finite set of normal surface solutions of $\mathcal T^*$.

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Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman