Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

Autor:	Kim, Joontae, Kim, Seongchan, Kwon, Myeonggi
Rok vydání:	2018
Předmět:	Mathematics - Symplectic Geometry Mathematics - Dynamical Systems 53D40 37C27 37J05
Druh dokumentu:	Working Paper
DOI:	10.1017/etds.2020.144
Popis:	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. Comment: 42 pages, 4 figures, final version, to appear in Ergodic Theory and Dynamical Systems
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.08099 Zobrazit plný text záznamu View this record from Arxiv