[Binghamton Geometry/Topology Seminar] Geometry/Topology Seminar

[Christoforos Neofytidis]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

   Date: Thursday, October 20th, 2016

   Time: 2.50 pm

   Place: Whitney Hall, Room 100E

   Speaker: Thomas Barthelmé (Queen's University)

   Title: Counting orbits of Anosov flows in free homotopy classes

Abstract: (Joint work with Sergio Fenley)
Since Margulis and Bowen gave an estimate of the growth rate of periodic
orbits of Anosov flow, there has been a lot of research furthering
counting questions. If one consider only Anosov flows, these developments
have been either into giving more precise estimates or into counting
periodic orbits given a homological constraint, i.e., counting periodic
orbits that are in the same fixed homology class. I will talk here about a
third direction: Despite what one might think when considering the most
classical examples of Anosov flows, a lot of Anosov flows (maybe most) in
3-manifolds are such that some periodic orbits are freely homotopic to
infinitely many other. It is therefore legitimate to ask whether one can
give an estimate of the growth rate of periodic orbits inside an infinite
free homotopy class. I will explain how one can use the geometry and
topology of Anosov flows in 3 manifolds to obtain such estimates. As a
corollary, we get an answer to the following question, asked by Plante and
Thurston in 1972: If M is a manifold supporting an Anosov flow, does the
number of conjugacy classes in the fundamental group grows exponentially
fast with the length of the shortest orbit representative?

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem