Finiteness conditions in covers of Poincaré duality spaces

2013/01/17 by Jonathan A. Hillman, Hillman, Jonathan A.
Mathematics · #57P10 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57P10

paper · pdf · doi:10.48550/arxiv.1301.3972

v2: Theorem 7 added at end

openalex publication_date 2013/01/17 · arxiv created 2015/04/27 · arxiv updated 2015/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A closed 4-manifold (or, more generally, a finite PD₄-space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a PD₃-complex.

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