Hello everyone,

This week we have Hannah Turner in town. She will be speaking at 3:30 tomorrow on Generalizing the (fractional) Dehn twist coefficient.

The title and abstract are below.

Also, next week Eric Sedgwick is in town. There is a slight conflict with the 3:30 time slot next week, so I wanted to check with everyone to see what conflicts would arise if the October 4 talk was moved to 2:30. Let me know if you can make that adjusted time on October 4th or if you have a conflict.

Title: Generalizing the (fractional) Dehn twist coefficient. Speaker: Hannah Turner, Georgia Tech Date: Sep 27, 2022 Time: 3:30 PM Room: MSCS 445 Abstract: The fractional Dehn twist coefficient (FDTC) is a rational number associated to a mapping class on a (finite-type) surface with boundary. This 2-dimensional invariant has many applications to 3-manifold topology and contact geometry. One way to think of the FDTC is as a real-valued function on the mapping class group of a surface with many nice properties. In this talk, we will give sufficient conditions on a more general group to admit a function which behaves like the FDTC. In particular, we use this to generalize the FDTC to infinite-type surfaces (with boundary); in this setting, we show that the ”fractional” Dehn twist coefficient need not be rational. This is joint work with Peter Feller and Diana Hubbard.

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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