|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'502'364
Articles rated: 2609
23 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Non-contractible periodic orbits, Gromov invariants, and Floer-theoretic torsions | | Yi-Jen Lee
; | | Date: |
20 Aug 2003 | | Subject: | Symplectic Geometry | math.SG | | Abstract: | 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. | | Source: | arXiv, math.SG/0308185 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER