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arXiv · 1811.08099

Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

Joontae Kim·Seongchan Kim·Myeonggi Kwon
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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 starshaped hypersurfaces in $\mathbb{R}^{2n}$ 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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Joontae Kim, Seongchan Kim, Myeonggi Kwon. 2018-11-20. Equivariant wrapped Floer homology and symmetric periodic Reeb orbits. https://doi.org/10.1017/etds.2020.144

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