School of Mathematical Sciences
Monday, March 16, 2015
Schreiber 006, 12:15
A geometric refinement of the fundamental group of a surface
Abstract: The fundamental
group of a topological space is among the first invariants one
encounters in topology. Here “invariant” means that two homeomorphic
spaces have the same fundamental group. More precisely, every
homeomorphism of spaces induces an isomorphism of fundamental groups.
For compact manifolds of dimension at most two, there is a remarkable
converse due to (in dimension 2) Dehn, Nielsen and Baer: Every
isomorphism of fundamental groups is induced by a homeomorphism. This
property fails for surfaces with boundary. However, as we will explain
in this talk, one can use hyperbolic geometry to construct an
enhancement of the fundamental group of such a surface, which is still
a topological invariant and for which a version of the
Dehn-Nielsen-Baer theorem holds.
The talk is based on joint work with Gabi Ben Simon, Marc Burger, Alessandra Iozzi and Anna Wienhard.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006