Pseudocycles and Integral Homology

2006/05/18 by Aleksey Zinger, Zinger, Aleksey · 1 citation
Mathematics · #55N99 #57R95 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AT #math.SG #msc:55N99 #msc:57R95

paper · pdf · doi:10.48550/arxiv.math/0605535

28 pages, 2 figures; a long technical construction has been simplified

openalex publication_date 2006/05/18 · arxiv created 2006/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a natural isomorphism between the set of equivalence classes of pseudocycles and the integral homology groups of a smooth manifold. Our arguments generalize to settings well-suited for applications in enumerative algebraic geometry and for construction of the virtual fundamental class in the Gromov-Witten theory.

Citations

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds

Cited by

• Equivalence between Gromov-Witten invariants: Domain dependent perturbation and Kuranishi structure approaches

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