The first meeting of the Seminar in the year 2008/09.
Monday September 22nd, 13:00, CRM Small room
Speaker: Jonathan Hillman, University of Sydney
Title: Indecomposable PD3 Complexes
Abstract: $PD$-complexes model the homotopy theory of manifolds. In dimension 3, the unique factorization theorem holds in the sense that a $PD3$-complex is a connected sum if and only if its fundamental group is a free product, and the indecomposables are either aspherical or have virtually free fundamental group [Tura'ev, Crisp]. However in contrast to the 3-manifold case the group of an indecomposable may have infinitely many ends (i.e., not be virtually abelian). We shall sketch the construction of one such example, and outline some recent work using only elementary group theory that imposes strong restrictions on any other such examples.
