Notes on exploded manifolds and a tropical gluing formula for Gromov-WItten invariants
Brett Parker
TL;DR
This paper discusses exploded manifolds and introduces a tropical gluing formula to compute Gromov-Witten invariants in degenerating families, providing a new approach to degeneration formulas in symplectic geometry.
Contribution
It presents a tropical gluing formula for Gromov-Witten invariants within the framework of exploded manifolds, advancing the understanding of degeneration formulas.
Findings
Derived a tropical gluing formula for Gromov-Witten invariants
Connected exploded manifolds with tropical geometry techniques
Provided a new degeneration formula for normal-crossing degenerations
Abstract
Notes for a short lecture series, covering exploded manifolds, the moduli stack of curves in exploded manifolds, and a tropical gluing formula for Gromov-Witten invariants: a gluing formula providing a degeneration formula for Gromov-Witten invariants in normal-crossing degenerations. I gave the original lecture series in April 2016 at the Simons Center for Geometry and Physics at Stonybrook. Video of the lectures is available on the SCGP website, http://scgp.stonybrook.edu/video_portal/video.php?id=2595
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology