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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.
Parker, Brett 1
@article{GT_2019_23_4_a4, author = {Parker, Brett}, title = {Holomorphic curves in exploded manifolds: virtual fundamental class}, journal = {Geometry & topology}, pages = {1877--1960}, publisher = {mathdoc}, volume = {23}, number = {4}, year = {2019}, doi = {10.2140/gt.2019.23.1877}, url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2019.23.1877/} }
TY - JOUR AU - Parker, Brett TI - Holomorphic curves in exploded manifolds: virtual fundamental class JO - Geometry & topology PY - 2019 SP - 1877 EP - 1960 VL - 23 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/gt.2019.23.1877/ DO - 10.2140/gt.2019.23.1877 ID - GT_2019_23_4_a4 ER -
Parker, Brett. Holomorphic curves in exploded manifolds: virtual fundamental class. Geometry & topology, Tome 23 (2019) no. 4, pp. 1877-1960. doi : 10.2140/gt.2019.23.1877. http://geodesic.mathdoc.fr/articles/10.2140/gt.2019.23.1877/
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