Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

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...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2022-05, Vol.42 (5), p.1708-1763
Main Authors: KIM, JOONTAE, KIM, SEONGCHAN, KWON, MYEONGGI
Format: Article
Language:English
Subjects:
Conjugation
Geometry
Homology
Hyperspaces
Lower bounds
Orbits
Original Article
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Summary: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 ${\mathbb {R}}^{2n}$ 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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2020.144