$P{D}_4$-complexes and 2-dimensional duality groups

Abstract

This paper is a synthesis and extension of three earlier papers on $P{D}_4$-complexes $X$ with fundamental group $\pi$ such that $c.d.\pi =2$ and $\pi$ has one end. Our goal is to show that the homotopy types of such complexes are determined by $\pi$, the Stiefel-Whitney classes and the equivariant intersection pairing on ${\pi }_2(X)$. We achieve this under further conditions on $\pi$.

arXiv admin note: substantial text overlap with arXiv:0712.1069. In v7 it is shown that strongly minimal $P{D}_4$-complexes are $\chi$-minimal, while strongly minimal is equivalent to order minimal if and only if $c.d.\pi \le 2$. In v.8 orientation condition removed in final theorem

References in corpus (5)

• Poincare duality complexes in dimension four
• Strongly minimal PD4-complexes
• Homotopy classification of $P{D}_4$-complexes relative an order relation
• Poincaré duality complexes with highly connected universal cover
• Poincare Duality Complexes with Highly Connected Universal Covers