Hello Topologists and Friends of Topology,
We will have a seminar this Thursday (MSCS 514 at 3:30) given by our very own Trent Schirmer.
Title: Splittings of 3-manifolds versus splittings of groups.
Abstract: Recent work of mine and Jesse's has shown that "high distance" free decomposing surfaces properly embedded in 3-manifolds with non-empty boundary exert considerable control over the appearance of other incompressible surfaces and Heegaard splittings in the manifold. These incompressible surfaces induce presentations of the fundamental group of the three manifold as a free product amalgamated over a subgroup whose word length is ``persistently" large with respect to a minimal generating set of each of the factors. I discuss the meaning of this.