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

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

2006-07-31

arxiv.org/abs/math/0607808v3

Mathematics

Algebraic Geometry

17 pages, LaTeX, uses Paul Taylor's diagrams package diagrams.sty Version 2: exposition streamlined, references added. Final v

Scientific paper

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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