Year: 2025
Type: preprint
Abstract: In this paper the cosheaf homology is investigated from different viewpoints: the behavior under site morphisms, connections with Cech homology via spectral sequences, and description of cosheaf homology using hypercoverings. It is proved that in the case of Hausdorff paracompact spaces, the cosheaf homology in general is isomorphic to the Cech homology, and for a constant cosheaf is isomorphic to the shape pro-homology. In the case of Alexandroff spaces, including finite and locally finite spaces, the cosheaf homology is isomorphic to the singular homology.
Source: arXiv (Cornell University)
Author: Prasolov, Andrei V.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415064857
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