Non-contractible periodic orbits, Gromov invariants, and Floer-theoretic torsions
| dc.creator | Lee, Yi-Jen | |
| dc.date | 2003-08-19 | |
| dc.date | 2003-09-03 | |
| dc.date.accessioned | 2026-07-07T05:00:29Z | |
| dc.date.available | 2026-07-07T05:00:29Z | |
| dc.description | In a previous paper, the author introduced a Floer-theoretic torsion invariant I_F, which roughly takes the form of a product of a power series counting perturbed pseudo-holomorphic tori, and the Reidemeister torsion of the symplectic Floer complex. We pointed out the formal resemblance of I_F with a generating function of genus 1 Gromov invariant; furthermore, for heuristic reasons one also expects a relation with the 1-loop generating function in the A-model side of mirror symmetry, which counts genus 1 holomorphic curves. The present article makes this expected relation precise in the simplest cases, in two variants of the I_F defined in the earlier work: the lagrangian intersection version, I_F(L, L'), and an S^1-equivariant version, I_F^{S^1}. As a by-product, we obtain some existence results of noncontractible periodic orbits in symplectic dynamics. For example, the results of Gatien-Lalonde are extended to a much wider class of manifolds. The two versions I_F(L, L') and I_F^{S^1} are only minimally developed in this paper, leaving fuller accounts to future work. The lagrangian intersection version, I_F(L, L'), should be viewed as a simplest example of a rigorous definition of the higher-loop ``open Gromov-Witten invariants'' proposed by physicists. | |
| dc.description | 73 pages, with 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0308185 | |
| dc.identifier | http://arxiv.org/abs/math/0308185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68347 | |
| dc.subject | Symplectic Geometry | |
| dc.title | Non-contractible periodic orbits, Gromov invariants, and Floer-theoretic torsions | |
| dc.type | text |