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arXiv · 1301.5454

Seidel elements and potential functions of holomorphic disc counting

Eduardo Gonzalez·Hiroshi Iritani
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Abstract

Let M be a symplectic manifold equipped with a Hamiltonian circle action and let L be an invariant Lagrangian submanifold of M. We study the problem of counting holomorphic disc sections of the trivial M-bundle over a disc with boundary in L through degeneration. We obtain a conjectural relationship between the potential function of L and the Seidel element associated to the circle action. When applied to a Lagrangian torus fibre of a semi-positive toric manifold, this degeneration argument reproduces a conjecture (now a theorem) of Chan-Lau-Leung-Tseng relating certain correction terms appearing in the Seidel elements with the potential function.

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Eduardo Gonzalez, Hiroshi Iritani. 2015-09-07. Seidel elements and potential functions of holomorphic disc counting. https://doi.org/10.2748/tmj%2F1505181621

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