Givental's Lagrangian Cone and S^1-Equivariant Gromov-Witten Theory
Abstract
Description
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.
17 pages, LaTeX, uses Paul Taylor's diagrams package diagrams.sty Version 2: exposition streamlined, references added. Final version; to appear in Mathematical Research Letters
17 pages, LaTeX, uses Paul Taylor's diagrams package diagrams.sty Version 2: exposition streamlined, references added. Final version; to appear in Mathematical Research Letters