2001/11/20 by Peter J. Kahn, Kahn, Peter J. · 1 citation
Mathematics · #55N35 #57N65 #57R17 #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:55N35 #msc:57N65 #msc:57R17
paper · pdf · doi:10.48550/arxiv.math/0111223
35 pages
arxiv created 2001/11/20 · openalex publication_date 2001/11/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a pseudocycle is introduced by McDuff and Salamon (J-holomorphic curves and quantum cohomology, University Lecture Series, Vol. 6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and quantum cohomology. This paper studies the bordism groups of pseudocycles, called pseudohomology groups. These are shown to satisfy the Eilenberg-Steenrod axioms. For smooth compact manifold pairs, it is proved that pseudohomology is naturally equivalent to homology. Easy examples show that this equivalence does not extend to the case of non-compact manifolds.