The E-cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T2n

Starostka, Maciej and Waterstraat, Nils (2017) The E-cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T2n. arxiv, . (Submitted) (Full text available)

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https://arxiv.org/abs/1708.09631

Abstract

We give a new proof of the strong Arnold conjecture for 1-periodic solutions of Hamiltonian systems on tori, that was first shown by C. Conley and E. Zehnder in 1983. Our proof uses other methods and is shorter than the previous one. We first show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals. Then an existence result for the E-cohomological Conley index, which applies to the setting of the Arnold conjecture, paves the way to a new proof of it on tori.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology > QA612 Algebraic topology
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Nils Waterstraat
Date Deposited: 13 Oct 2017 09:56 UTC
Last Modified: 17 Oct 2017 08:37 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/63985 (The current URI for this page, for reference purposes)
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