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Myeonggi, Kwon
기하학 수리물리 연구단
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Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

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Title
Equivariant wrapped Floer homology and symmetric periodic Reeb orbits
Author(s)
Kim, Joontae; Kim, Seongchan; Myeonggi Kwon
Publication Date
2021-02
Journal
Ergodic Theory and Dynamical Systems, pp.1 - 56
Publisher
Cambridge University Press
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 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.
URI
https://pr.ibs.re.kr/handle/8788114/9213
DOI
10.1017/etds.2020.144
ISSN
0143-3857
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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