### Bea Bleile

University of Sydney

### Homotopy classification and realization
of Poincaré duality pairs in dimension
three.

**Friday 1st, November 12:05-12:55pm,
Carslaw 373. **
Poincaré duality complexes are homotopy
generalizations of manifolds and Poincaré
duality pairs are homotopy generalizations of
manifolds with boundary.

In 1977 Hendriks gave a complete set of homotopy
invariants for three--dimensional Poincaré duality
complexes. Turaev provided an alternative proof of
Hendriks' classification theorem as well as necessary
and sufficient conditions for the invariants to be
realized by a three--dimensional Poincaré duality
complex.

This talk shows how Turaev's proof of the classification
theorem can be generalized to Poincaré duality pairs
and indicates how one may attempt to generalize the
realization theorem.