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Genus zero Gromov-Witten axioms via Kuranishi atlases

2016/01/15 by Robert Castellano, Castellano, Robert
Mathematics · #53D05 #53D45 #57R17 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D05 #msc:53D45 #msc:57R17

paper · pdf · doi:10.48550/arxiv.1601.04048

38 pages

arxiv created 2016/01/15 · openalex publication_date 2016/01/15 · arxiv updated 2016/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Kuranishi atlas is a structure used to build a virtual fundamental class on moduli spaces of J-holomorphic curves. They were introduced by McDuff and Wehrheim to resolve some of the challenges in this field. This paper completes the construction of genus zero Gromov-Witten invariants using Kuranishi atlases and proves the Gromov-Witten axioms of Kontsevich and Manin. To do so, we introduce the notion of a transverse subatlas, a useful tool for working with Kuranishi atlases.

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