
Jonathan Hillman
University of Sydney
Decomposition of PD_{3}complexes
Friday 15th October, 12:0512:55pm,
Carslaw 175.
Every closed orientable 3manifold has an essentially unique
factorization as a connected sum of prime 3manifolds, which
either have finite fundamental group or are aspherical or
are homeomorphic to S^{1} × S^{2}.
As PD_{n}complexes model the homotopy type of nmanifolds
it is natural to ask whether a similar result holds for
PD_{3}complexes.
Turaev showed that a PD_{3}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 PD_{3}complex whose fundamental
group is virtually free but not virtually cyclic.
This represents a departure from what 3manifold theory
would suggest, and is a counterexample to a question
raised by C.T.C.Wall in 1967.







