Kontsevich-Soibelman Wall Crossing Formula and Holomorphic Disks
Vito Iacovino
TL;DR
This paper introduces rational invariants counting holomorphic disks on hyperkähler manifolds and provides a straightforward proof of the Kontsevich-Soibelman Wall Crossing Formula for these invariants.
Contribution
It defines new rational invariants for holomorphic disks and offers a direct proof of the wall crossing formula in this context.
Findings
Defined rational invariants counting holomorphic disks
Provided a simple proof of the wall crossing formula
Confirmed the invariants satisfy the Kontsevich-Soibelman formula
Abstract
We define rational numbers counting holomorphic disks bounding a complex lagrangian submanifold on a hyperkhaler manifold of real dimension four. We provide a simple a direct proof of Kontsevich-Soibelman Wall Crossing Formula for these rational invariants.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Geometric and Algebraic Topology