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Algebra Seminar
University of Sydney> Maths & Stats> Research> Algebra Seminar> Abstracts


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.