Geometry, Topology and Dynamics Seminar
Igor Belegradek
Georgia Tech
Aspherical manifold and relative hyperbolization
Abstract: In the first half of the talk I shall explain how to build aspherical
manifolds using relative strict hyperbolization of polyhedra. As I recently
showed, these manifolds share many topological properties with noncompact finite
volume manifolds of pinched negative curvature. This topic will be discussed in
more detail in my talk on November 17 at the University of Chicago. Here I shall
focus on the following applications:
1. Any closed aspherical triangulated n-manifold with hyperbolic fundamental
group is a retract of some closed aspherical triangulated (n+1)-manifold with
hyperbolic fundamental group. This gives a new source of closed aspherical
manifolds with hyperbolic fundamental groups.
2. There is a closed aspherical manifold with nonzero simplicial volume whose
fundamental group has unsolvable word problem. Examples of groups with solvable
word problem include automatic groups, CAT(0)-groups, residually finite groups,
and linear groups over any commutative ring.
Wednesday November 16, 2005 at 3:00 PM in SEO 427