Department of Mathematics

Student Geometry/Topology

  •  Michael Shultz
  •  The homology polynomial and pseudo-Anosov braids
  •  10/17/2018
  •  4:10 PM - 5:00 PM
  •  A202 Wells Hall

Every orientation preserving homeomorphism of a compact, connected, orientable surface S is isotopic to a representative that is periodic, reducible, or pseudo-Anosov (pA). In the last case, the representative is neither periodic nor reducible and the surface admits two (singular) transverse measured foliations. The pA representative "stretches" with respect to one of these measures by a number called the stretch factor. The homology polynomial, introduced by Birman, Brinkmann, and Kawamuro, is an invariant of the isotopy class and contains the stretch factor as it's largest real root. It can also distinguish some distinct pA maps with the same stretch factor. In this talk I will discuss the ideas behind the homology polynomial and how it is obtained. As time permits I will discuss some examples involving pA braids and touch on a connection with the Burau representation.

 

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Michigan State University
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