Thursday, September 12, 2012 at 3pm in CH (Cockins Hall) 240
Mike Davis, OSU
Aspherical manifolds that cannot be triangulated
Abstract
By a result of Manolescu there are topological closed n-manifolds that cannot be triangulated for each n greater than or equal to 5. We show that for n greater than or equal to 6, we can choose such manifolds to be aspherical. This is joint work with jim Fowler and Jean Lafont.
Thursday, September 19, 2013 at 1:50 pm in CH (Cockins Hall) 240
Kathyrn Mann, University of Chicago
Components of representation spaces
Abstract
Let G be a group of homeomorphisms of the circle, and
\Gamma the fundamental group of a closed surface.
The representation space Hom(\Gamma, G) is a basic example
in geometry and topology: it parametrizes circle bundles
over the surface with structure group G, and actions of
\Gamma on the circle with regularity given by G. A
remarkable theorem of W. Goldman says that for G =
PSL(2,R), the components of Hom(\Gamma, G) are completely
determined by the Euler number, a classical
invariant. By contrast, the space Hom(\Gamma,
Homeo+(S^1)) is relatively unexplored -- in fact it is an
open question whether it has finitely many or infinitely
many components.
In this talk, I'll motivate the study of representation
spaces, and then report on recent work and new tools to
distinguish connected components of Hom(\Gamma,
Homeo+(S^1)). In particular, this work gives a new
lower bound on the number of components (more than are
distinguished by the Euler number alone) and identifies
many representations which exhibit surprising rigidity.
Thursday, September 26, 2013 at 1:50 pm in CH (Cockins Hall) 240
David Simmons, OSU
Geometry and dynamics of groups acting on Gromov hyperbolic metric spaces
Abstract
In this talk, I will discuss two theorems about groups acting by isometries on Gromov hyperbolic metric spaces. The first theorem is a generalization of a theorem of Bishop and Jones ('97) and Paulin ('97) to this setting. The second is a construction of Patterson-Sullivan measures in a setting where compactness is not assumed. Both theorems are part of an ongoing collaboration with Tushar Das (University of Wisconsin - La Crosse) and Mariusz Urbański (University of North Texas).
Thursday, November 21, 2013 at 1:50 pm in CH (Cockins Hall) 240
Olympia Talelli, University of Athens
On characteristic modules for groups
Abstract
A characteristic module for a group G
is a Z-free ZG-module, of finite projective dimension
over ZG, with nontrivial elements invariant under the
action of G. We present the relation of the
characteristic modules to the Gorenstein dimension of
G, the generalized cohomological dimension of
G and proper actions of G.
Thursday, April 17, 2014 at 1:50 pm in MA 317
Tam Nguyen Phan, University of Binghamton
Ends of finite volume, negatively curved manifolds
Abstract
Let M be an oriented, noncompact, complete, Riemannian manifold. Gromov proved that if the sectional curvature of M negative and bounded, and if the volume of M is finite, then M is homeomorphic to the interior of a compact manifold \overline{M} with boundary B. I will discuss the question what manifold B can be. I will prove that when M has dimension 4, each boundary component of \overline{M} is aspherical.