Borel-Moore homology and cap product operations

2016/12/16 by Masaki Hanamura, Hanamura, Masaki · 1 citation
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Amino acid #Biology #Cellular homology #FOS: Mathematics #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematics #Pure mathematics #Relative homology #Topological and Geometric Data Analysis #math.AG #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.1612.05407

37 pages

openalex publication_date 2016/12/16 · arxiv created 2022/02/28 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, for a simplicial complex, the supported cap product operation on Borel-Moore homology coincides with the supported cap product on simplicial homology. For this purpose we introduce the supported cap product for locally finite singular homology, and compare the cap product on the three homology theories.

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