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Title:
Lusternik-Schnirelmann Theory, the Shift Operator and Closed Reeb Orbits
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Abstract:
In this talk we focus on the role of Lusternik-Schnirelmann theory in multiplicity results for closed Reeb orbits. We develop a variant of this theory for the shift operator in the equivariant Floer and symplectic homology and prove that spectral invariants are strictly decreasing under the action of the shift operator when periodic orbits are isolated. We then show how this fact is used in the proofs of multiplicity results for simple closed Reeb orbits without non-degeneracy. The talk is based on a joint work with Basak Gurel and I’ll try to give at least some technical details of the constructions and proofs.
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