Holomorphic curves in exploded manifolds virtual fundamental class

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Abstract

We define Gromov–Witten invariants of exploded manifolds. The technical heart of this paper is a construction of a virtual fundamental class [K] of any Kuranishi category K (which is a simplified, more general version of an embedded Kuranishi structure). We also show how to integrate differential forms over [K] to obtain numerical invariants, and push forward such differential forms over suitable maps. We show that such invariants are independent of any choices, and are compatible with pullbacks, products and tropical completion of Kuranishi categories. In the case of a compact symplectic manifold, this gives an alternative construction of Gromov–Witten invariants, including gravitational descendants.

Original languageEnglish
Pages (from-to)1877–1960
Number of pages84
JournalGeometry and Topology
Volume23
Issue number4
DOIs
Publication statusPublished - 17 Jun 2019

Keywords

  • Exploded manifolds
  • Gromov–Witten invariants
  • Holomorphic curves
  • Virtual fundamental class

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