University of Sydney
Decomposition of PD3-complexes
Friday 15th October, 12:05-12:55pm,
Every closed orientable 3-manifold has an essentially unique
factorization as a connected sum of prime 3-manifolds, which
either have finite fundamental group or are aspherical or
are homeomorphic to S1 × S2.
As PDn-complexes model the homotopy type of n-manifolds
it is natural to ask whether a similar result holds for
Turaev showed that a PD3-complex P is a connected sum
if and only if its fundamental group is a free product,
and Crisp showed that if P is indecomposable then it is
aspherical or has virtually free fundamental group.
We shall review briefly their results, and give an example
of an indecomposable PD3-complex whose fundamental
group is virtually free but not virtually cyclic.
This represents a departure from what 3-manifold theory
would suggest, and is a counter-example to a question
raised by C.T.C.Wall in 1967.