Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1811.08099

Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

Joontae Kim·Seongchan Kim·Myeonggi Kwon
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.SGmath.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Joontae Kim, Seongchan Kim, Myeonggi Kwon. 2021-02-04. Equivariant wrapped Floer homology and symmetric periodic Reeb orbits. https://doi.org/10.1017/etds.2020.144

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

New systems of log-canonical coordinates on $SL(2, \mathbb{C})$ character varieties of compact Riemann surfaces

We construct new sets of log-canonical coordinates on the $SL(2, \mathbb{C})$ character variety of compact Riemann surfaces. These are labelled by families of $1\leq m\leq 3g-3$ non-intersecting simple loops on the Riemann surface and are obtained by combining complexified shear-type with length/twist-type coordinates. In the case $m=3g-3$ the loops define a trinion decomposition of the Riemann surface, and our coordinates are closely related to the (complexified) Fenchel-Nielsen ones.

math.SG↗
arXiv2026

Moment Lagrangians, unobstructedness and symplectic groupoids

Moment Lagrangian $L_μ$ is a Lagrangian in $T^*G^- \times Y^- \times Y$ associated to a Hamiltonian $G$-space $Y$ with a moment map $μ$. In this paper, we prove that $L_μ$ is tautologically unobstructed under mild assumptions on $Y$. As a key ingredient in the proof, we constructed a new symplectic groupoid structure on $T^*G^- \times Y^- \times Y$ over $G\times Y$ for which $L_μ$ is simultaneously the unit and the fixed locus of the inversion, which might be of independent interest.

math.SG↗
arXiv2026

Stratifications associated to generic closed two-forms and stratified $L_\infty$ spaces

Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an $L_\infty$ algebra attached to the foliation de-Rham complex associated to the null foliation of the corresponding presymplectic structure. The main purpose of the present paper is to extend this study of $L_\infty$ structures to the case of generic closed two-forms on arbitrary smooth manifolds as a stratified $L_\infty$ space. We first prove that there exists a residual subset of closed 2-forms, which we denote by $Z^2_{reg}(M) \subset Z^2(M)$, such that any element $ω$ therefrom admits a Whitney stratification each of whose strata is a presymplectic manifold. We then associate an $L_\infty$ space to each stratum (and to its tubular neighborhood) and glue the collection of $L_\infty$ spaces to a global stratified $L_\infty$ space by the coordinate atlas consisting of $L_\infty$ morphisms, which is a collection of $L_\infty$ morphisms, not necessarily of quasi-isomorphisms.

math.SG↗