Quantum D-modules and equivariant Floer theory for free loop spaces
| dc.creator | Iritani, Hiroshi | |
| dc.date | 2004-10-22 | |
| dc.date | 2006-03-18 | |
| dc.date.accessioned | 2026-07-07T09:21:17Z | |
| dc.date.available | 2026-07-07T09:21:17Z | |
| dc.description | 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, it follows that equivariant Floer cohomology defined here is isomorphic to the quantum cohomology D-module. | |
| dc.description | 37 pages, the original version was written in June,2003, v2 added e-mail address, v3 final version | |
| dc.identifier | https://arxiv.org/abs/math/0410487 | |
| dc.identifier | http://arxiv.org/abs/math/0410487 | |
| dc.identifier | Math. Z. 252 (3) (2006), pp.577--622 | |
| dc.identifier | doi:10.1007/s00209-005-0867-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154969 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D45 (Primary) 14N35, 53D40 (Secondary) | |
| dc.title | Quantum D-modules and equivariant Floer theory for free loop spaces | |
| dc.type | text |