Global Kuranishi charts and a product formula in symplectic Gromov-Witten theory
Amanda Hirschi, Mohan Swaminathan
TL;DR
This paper constructs global Kuranishi charts for moduli spaces of stable pseudoholomorphic maps in all genera and uses them to establish a product formula for symplectic Gromov-Witten invariants, leading to a K"unneth formula for quantum cohomology.
Contribution
It introduces a method to build global Kuranishi charts for all genera and applies this to derive a product formula in symplectic Gromov-Witten theory.
Findings
Proved a product formula for symplectic Gromov-Witten invariants.
Established a K"unneth formula for quantum cohomology.
Constructed global Kuranishi charts for all genera.
Abstract
We construct global Kuranishi charts for the moduli spaces of stable pseudoholomorphic maps to a closed symplectic manifold in all genera. This is used to prove a product formula for symplectic Gromov-Witten invariants. As a consequence we obtain a K\"unneth formula for quantum cohomology.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Algebra and Geometry · Geometry and complex manifolds