Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                             Spring  2016


   Organizers:  Gennadi Kasparov, Ioana Suvaina, Rares Rasdeaconu

   Fridays, 3:10-4:00pm in SC 1310 (unless otherwise noted)




Friday, February 5th

Speaker: Kun Wang, Vanderbilt University

Title: Topological rigidity for closed aspherical manifolds fibering over the unit circle

Abstract: The Borel conjecture in manifold topology predicts that every closed aspherical manifold is
topologically rigid, i.e. every homotopy equivalence between any two closed aspherical manifolds
is homotopic to a homeomorphism. There are variants of the Borel conjecture, such as the simple
Borel conjecture and the bordism Borel conjecture, corresponding to other types of topological rigidity. 
In this talk, I consider topological rigidity for closed aspherical manifolds that fiber over the unit circle.
We show that, in dimensions greater than or equal to 5, both the simple Borel conjecture and the
bordism Borel conjecture hold for such an aspherical manifold, provided the fundamental group
of the fiber belongs to a large class of groups, including Gromov hyperbolic groups, CAT(0) groups,
and lattices in virtually connected lie groups. The main ingredients in proving this rigidity result
are some general results that we obtain in algebraic L-theory.  These results also have some applications
to the Novikov conjecture.


Friday, February 12th

Speaker: Matthieu Jacquemet, Vanderbilt University

Title: Around hyperbolic Coxeter polyhedra I

Abstract: Unlike their spherical and Euclidean cousins, hyperbolic Coxeter polyhedra do not exist
any more in higher dimensions, and are far from being classified. In this first talk, we intend to give
a survey on their existence and classification. No particular background will be assumed.


Friday, February 19th

Speaker: Matthieu Jacquemet, Vanderbilt University

Title: Around hyperbolic Coxeter polyhedra II

Abstract: In this second talk, we shall discuss recent results related to two natural classes of
hyperbolic polyhedra : simplices, and Coxeter cubes. It time permits, we shall outline a couple
of open problems which could be attacked by using these new results.








 

 Old Seminar Web-Pages: Fall 2009, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Fall 2015