Quantum D-modules and equivariant Floer theory for free loop spaces |
| |
Authors: | Hiroshi Iritani |
| |
Affiliation: | (1) Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan |
| |
Abstract: | The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry'. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohomology for the universal cover of the free loop space. First, motivated by the work of Guest, we formulate the notion of ``abstract quantum D-module' which generalizes the D-module defined by the small quantum cohomology algebra. Second, we define the equivariant Floer cohomology of toric complete intersections rigorously as a D-module, using Givental's model. This is shown to satisfy the axioms of abstract quantum D-module. By Givental's mirror theorem [Giv3], it follows that equivariant Floer cohomology defined here is isomorphic to the quantum cohomology D-module. |
| |
Keywords: | 53D45 14N35 53D40 |
本文献已被 SpringerLink 等数据库收录! |
|