[Binghamton Geometry/Topology Seminar] Geometry & Topology seminar

[somnath at math.binghamton.edu]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, October 10th, 2013

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson
Reading Room.

*Speaker: ** *Thomas Bathelmé (Tufts University)
*Title: *
Knot theory of R-covered Anosov flows on 3-manifolds: homotopy versus
isotopy of periodic orbits

*Abstract:* Anosov flows are uniformly hyperbolic flows: at each point
there is one exponentially contracting and one exponentially expanding
direction, with uniform rates. The classical examples of Anosov flows in
3-dimension are the geodesic flow of a negatively curved surface (which is
a flow on the unit tangent bundle of a surface of genus >1) and
suspensions of Anosov diffeomorphism (which gives a flow on a 3-torus).
But there are many more examples of Anosov flows on all sorts of
3-manifolds (including hyperbolic ones). In this talk, I will focus on one
type of "nice" Anosov flows; those such that there stable and unstable
foliations are R-covered (i.e., the leaf space of each foliations is
homeomorphic to R). Sergio Fenley proved that, if the manifold is
atoroidal, then homotopy class of periodic orbits contains infinitely many
distinct orbits. I will explain how, using the structure of the different
foliations associated to an Anosov flow, we can see that every orbits in
one homotopy class are in fact isotopic. This work is in collaboration
with Sergio Fenley.