Perfect Reeb flows and action-index relations

    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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