2022/10/12 by John R. Klein, Klein, John R.
Mathematics · #19J05 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Primary: 57P10 #Secondary: 16E20
paper · pdf · doi:10.48550/arxiv.2210.06580
openalex publication_date 2022/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let π be finitely presented group. Assuming that the reduced Grothendieck group K0(\Bbb Z[π]) has a non-trivial 2-divisible element, we construct a finitely dominated Poincaré space X with fundamental group π such that X is not homotopy finite. The dimension of X can be made arbitrarily large. Our proof relies on a result which says that every finitely dominated space possesses a stable Poincaré duality thickening.