Indecomposable $PD_3$-complexes

Jonathan Hillman (University of Sydney)

Monday 1st December, 2008 16:00-17:00 Mathematics Building, room 214


$PD$-complexes model the homotopy theory of manifolds. In dimension 3, the unique factorization theorem holds to the extent that a $PD_3$-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 cyclic). We shall sketch the construction of one such example, and outline some recent work using only group theory that imposes strong restrictions on any other such examples.

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