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On the filtered symplectic homology of prequantization bundles

Viktor L. Ginzburg

http://orcid.org/0000-0002-2932-8056

Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA

E-mail Address: ginzburg@ucsc.edu

Corresponding author.

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and

Jeongmin Shon

Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA

E-mail Address: jeshon@ucsc.edu

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https://doi.org/10.1142/S0129167X18500714Cited by:8 (Source: Crossref)

Abstract

We study Reeb dynamics on prequantization circle bundles and the filtered (equivariant) symplectic homology of prequantization line bundles, aka negative line bundles, with symplectically aspherical base. We define (equivariant) symplectic capacities, obtain an upper bound on their growth, prove uniform instability of the filtered symplectic homology and touch upon the question of stable displacement. We also introduce a new algebraic structure on the positive (equivariant) symplectic homology capturing the free homotopy class of a closed Reeb orbit — the linking number filtration — and use it to give a new proof of the non-degenerate case of the contact Conley conjecture (i.e. the existence of infinitely many simple closed Reeb orbits), not relying on contact homology.

Keywords:

AMSC: 53D40, 37J10, 37J45, 37J55

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