Title

Perfect Reeb flows and action-index relations

Authors

Authors

B. Z. Gurel

Comments

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Abbreviated Journal Title

Geod. Dedic.

Keywords

Periodic orbits; Contact forms; Reeb flows; Contact homology; COMPACT CONVEX HYPERSURFACES; SYMPLECTIC FIELD-THEORY; HAMILTONIAN; DIFFEOMORPHISMS; CLOSED CHARACTERISTICS; WEINSTEIN CONJECTURE; CONTACT; HOMOLOGY; PERIODIC POINTS; ENERGY SURFACES; MORSE-THEORY; DYNAMICS; Mathematics

Abstract

We study non-degenerate Reeb flows arising from perfect contact forms, i.e., the forms with vanishing contact homology differential. In particular, we obtain upper bounds on the number of simple closed Reeb orbits for such forms on a variety of contact manifolds and certain action-index resonance relations for the standard contact sphere. Using these results, we reprove a theorem due to Bourgeois, Cieliebak and Ekholm characterizing perfect Reeb flows on the standard contact three-sphere as non-degenerate Reeb flows with exactly two simple closed orbits.

Journal Title

Geometriae Dedicata

Volume

174

Issue/Number

1

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

105

Last Page

120

WOS Identifier

WOS:000348421600006

ISSN

0046-5755

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