Geometric Cycles in Floer Theory
Max Lipyanskiy
TL;DR
This paper develops a new version of Hamiltonian Floer Homology using semi-infinite cycles, offering a novel approach to prove the existence of critical points of the action functional.
Contribution
It introduces a semi-infinite cycle framework for Floer Homology, providing a new proof for critical point existence in Hamiltonian dynamics.
Findings
Established a semi-infinite cycle-based Floer Homology
Provided a new proof for critical points of the action functional
Enhanced understanding of Hamiltonian Floer theory
Abstract
We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals