$PD_4$-complexes and 2-dimensional duality groups
Geometric Topology
2026-05-14 v8
Abstract
This paper is a synthesis and extension of three earlier papers on -complexes with fundamental group such that and has one end. Our goal is to show that the homotopy types of such complexes are determined by , the Stiefel-Whitney classes and the equivariant intersection pairing on . We achieve this under further conditions on .
Cite
@article{arxiv.1303.5486,
title = {$PD_4$-complexes and 2-dimensional duality groups},
author = {Jonathan A. Hillman},
journal= {arXiv preprint arXiv:1303.5486},
year = {2026}
}
Comments
arXiv admin note: substantial text overlap with arXiv:0712.1069. In v7 it is shown that strongly minimal $PD_4$-complexes are $\chi$-minimal, while strongly minimal is equivalent to order minimal if and only if $c.d.\pi\leq2$. In v.8 orientation condition removed in final theorem