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Givental's Lagrangian Cone and S^1-Equivariant Gromov-Witten Theory

Tom Coates
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Abstract

In the approach to Gromov-Witten theory developed by Givental, genus-zero Gromov-Witten invariants of a manifold X are encoded by a Lagrangian cone in a certain infinite-dimensional symplectic vector space. We give a construction of this cone, in the spirit of S^1-equivariant Floer theory, in terms of S^1-equivariant Gromov-Witten theory of the product X \times P^1. This gives a conceptual understanding of the "dilaton shift": a change-of-variables which plays an essential role in Givental's theory.

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Tom Coates. 2007-10-25. Givental's Lagrangian Cone and S^1-Equivariant Gromov-Witten Theory. https://arxiv.org/abs/math/0607808

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