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TITLE Equivariant wrapped Floer homology and symmetric periodic Reeb orbits
KIAS AUTHORS Kim, Joontae,Kim, Joontae
JOURNAL ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2022
ARCHIVE https://doi.org/10.1017/etds.2020.144
ABSTRACT The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic properties. By a careful analysis of index iterations, we obtain a non-trivial lower bound on the minimal number of geometrically distinct symmetric periodic Reeb orbits on a certain class of real contact manifolds. This includes non-degenerate real dynamically convex star-shaped hypersurfaces in R-2n which are invariant under complex conjugation. As a result, we give a partial answer to the Seifert conjecture on brake orbits in the contact setting.
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