English

$PD_4$-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 PD4PD_4-complexes XX with fundamental group π\pi such that c.d.π=2c.d.\pi=2 and π\pi has one end. Our goal is to show that the homotopy types of such complexes are determined by π\pi, the Stiefel-Whitney classes and the equivariant intersection pairing on π2(X)\pi_2(X). We achieve this under further conditions on π\pi.

Keywords

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

R2 v1 2026-06-21T23:46:20.432Z