Borel-Moore homology and cap product operations
Masaki Hanamura
TL;DR
This paper demonstrates that the supported cap product operation on Borel-Moore homology aligns with that on simplicial homology for simplicial complexes, introducing a new supported cap product for locally finite singular homology.
Contribution
It introduces the supported cap product for locally finite singular homology and compares it with existing cap products across three homology theories.
Findings
Supported cap product on Borel-Moore homology matches that on simplicial homology.
Introduces supported cap product for locally finite singular homology.
Establishes equivalence of cap product operations across homology theories.
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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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models