2009/10/29 by Reinhard Diestel, Diestel, Reinhard, Philipp Sprüssel +1
Computer Science · Mathematics · Medicine · #05C63 (Secondary) #55N10 #55N40 (Primary) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Topological and Geometric Data Analysis #math.AT #math.CO #msc:05C63 #msc:55N10 #msc:55N40
paper · pdf · doi:10.48550/arxiv.0910.5650
23 pages; final version, to appear in Topology and its Applications
openalex publication_date 2009/10/29 · arxiv created 2011/05/25 · arxiv updated 2011/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original graph-theoretical definition could be captured in the usual language for homology theories, so as to make it applicable to more general spaces. In this paper we provide such a general topological framework: we define a homology theory which satisfies the usual axioms, but which maintains the special role for ends that has made this homology work so well for graphs.