The refined symplectic sum formula for Gromov-Witten invariants

Mohammad F. Tehrani; Aleksey Zinger

doi:10.1142/S0129167X20500329

The refined symplectic sum formula for Gromov-Witten invariants

Mohammad F. Tehrani
, Aleksey Zinger

Mathematics

Stony Brook University
University of Iowa

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We describe the extent to which Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants (GW-invariants) sharpens the usual symplectic sum formula. The key product operation on the target spaces for the refined invariants is specified in terms of abelian covers of symplectic divisors, making it suitable for studying from a topological perspective. We give several qualitative applications of this refinement, which include vanishing results for GW-invariants.

Original language	English
Article number	2050032
Journal	International Journal of Mathematics
Volume	31
Issue number	4
DOIs	https://doi.org/10.1142/S0129167X20500329
State	Published - Apr 1 2020

Keywords

Gromov-Witten invariants
rim tori refinement
symplectic sum formula

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10.1142/S0129167X20500329

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abstract = "We describe the extent to which Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants (GW-invariants) sharpens the usual symplectic sum formula. The key product operation on the target spaces for the refined invariants is specified in terms of abelian covers of symplectic divisors, making it suitable for studying from a topological perspective. We give several qualitative applications of this refinement, which include vanishing results for GW-invariants.",

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AB - We describe the extent to which Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants (GW-invariants) sharpens the usual symplectic sum formula. The key product operation on the target spaces for the refined invariants is specified in terms of abelian covers of symplectic divisors, making it suitable for studying from a topological perspective. We give several qualitative applications of this refinement, which include vanishing results for GW-invariants.

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KW - rim tori refinement

KW - symplectic sum formula

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The refined symplectic sum formula for Gromov-Witten invariants

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Keywords

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