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arXiv · 2209.10036

Pseudocycles for Borel-Moore Homology

Spencer Cattalani·Aleksey Zinger
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Abstract

Pseudocycles are geometric representatives for integral homology classes on smooth manifolds that have proved useful in particular for defining gauge-theoretic invariants. The Borel-Moore homology is often a more natural object to work with in the case of non-compact manifolds than the usual homology. We define weaker versions of the standard notions of pseudocycle and pseudocycle equivalence and then describe a natural isomorphism between the set of equivalence classes of these weaker pseudocycles and the Borel-Moore homology. We also include a direct proof of a Poincar\'e Duality between the singular cohomology of an oriented manifold and its Borel-Moore homology.

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Spencer Cattalani, Aleksey Zinger. 2022-09-20. Pseudocycles for Borel-Moore Homology. https://doi.org/10.1142/s1793525324500389

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