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Holomorphic curves in
exploded manifolds: virtual fundamental class
Brett Parker |
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Geometry & Topology 23 (2019) 1877–1960
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Abstract |
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We define Gromov–Witten invariants of exploded manifolds. The technical heart of this paper is a construction of a virtual fundamental class of any Kuranishi category (which is a simplified, more general version of an embedded Kuranishi structure). We also show how to integrate differential forms over 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. |
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Keywords
holomorphic curves, virtual fundamental class, exploded
manifolds, Gromov–Witten invariants
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Mathematical Subject Classification 2010
Primary: 53D45
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References |
Publication
Received: 29 June 2017
Revised: 10 September 2018
Accepted: 7 October 2018
Published: 17 June 2019
Proposed: Richard Thomas
Seconded: Jim Bryan, Dan Abramovich
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Authors |
| Brett Parker | |
| Monash University Melbourne, VIC Australia |
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