On the proper homotopy type of locally compact A²_n-polyhedra

2006/05/08 by Fernando Muro, Muro, Fernando
Mathematics · #18G15 #18G35 #18G50 #18G60 #55P15 #55P57 #55S05 #55S35 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18G15 #msc:18G35 #msc:18G50 #msc:18G60 #msc:55P15 #msc:55P57 #msc:55S05 #msc:55S35

paper · pdf · doi:10.48550/arxiv.math/0605213

100 pages

arxiv created 2006/05/08 · openalex publication_date 2006/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we address the classification problem for locally compact (n-1)-connected CW-complexes with dimension less or equal than n+2 up to proper homotopy type. We obtain complete classification theorems in terms of purely algebraic data in those cases where the representation type of the involved algebra is finite. For this we define new quadratic functors in controlled algebra and new homotopy and cohomology invariants in proper homotopy theory.

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