Fundamental Triples and Poincaré Duality Complexes with Highly Connected Universal Covers

Bea Bleile (University of New England)

Abstract

We begin with an overview of the classification of Poincaré duality complexes using fundamental triples. Applied to Poincaré duality complexes with highly connected universal covers this classification verifies the first part of a conjecture by Turaev. We then establish Turaev’s conjectures on realisation and splitting of such spaces.