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