Fundamental Triples and Poincare Duality Complexes with Highly Connected Universal Covers

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.