Reduced Open Gromov-Witten Invariants on HyperK\"aher Manifolds
Yu-Shen Lin
TL;DR
This paper introduces a new class of disc-counting invariants on hyperK"ahler manifolds that exhibit wall-crossing phenomena, potentially linking to generalized Donaldson-Thomas invariants and hyperK"ahler metric construction.
Contribution
It defines reduced open Gromov-Witten invariants with deformable boundary conditions on hyperK"ahler manifolds, highlighting their wall-crossing behavior and relation to Donaldson-Thomas invariants.
Findings
Invariants exhibit non-trivial wall-crossing phenomena.
Potential connection to generalized Donaldson-Thomas invariants.
Application to hyperK"ahler metric construction.
Abstract
We use the hyperK\"aler geometry define an disc-counting invariants with deformable boundary condition on hyperK\"ahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon and are expected to be the generalized Donaldson-Thomas invariants in the construction of hyperK\"ahler metric proposed by Gaiotto-Moore-Neitzke.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows