Weinstein Conjecture and GW Invariants
Gang Liu, Gang Tian
TL;DR
This paper links Gromov-Witten invariants to the existence of closed orbits in Hamiltonian systems and fully resolves the stabilized Weinstein conjecture.
Contribution
It establishes a general relationship between GW invariants and closed orbits, and provides a complete proof of the stabilized Weinstein conjecture.
Findings
GW invariants' nonvanishing implies closed orbits existence
Complete proof of the stabilized Weinstein conjecture
New insights into Hamiltonian dynamics
Abstract
In this paper, we establish a general relationship between the nonvanishing of GW invariants with the existence of the closed orbits of a Hamiltonian system. As an application, we completely solved the stabilized Weinstein conjecture.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Advanced Algebra and Geometry