Related papers: Lectures on Twisted Rabinowitz-Floer Homology
Rabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer associated with the Rabinowitz action functional introduced by Kai Cieliebak and Urs Frauenfelder in 2009. In our work, we consider a generalisation of this theory…
A contact manifold admittting a supporting contact form without contractible Reeb orbits is called hypertight. In this paper we construct a Rabinowitz Floer homology associated to an arbitrary supporting contact form for a hypertight…
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…
This paper extends the definition of Rabinowitz Floer homology to non-compact hypersurfaces. We present a general framework for the construction of Rabinowitz Floer homology in the non-compact setting under suitable compactness assumptions…
This thesis considers fillable contact structures on odd-dimensional manifolds. For that purpose, Rabinowitz-Floer homology (RFH) is used which was introduced by Cieliebak and Frauenfelder in 2009. A major part of the thesis is devoted to…
Consider the cotangent bundle of a Riemannian manifold $(M,g)$ of dimension 2 or more, endowed with a twisted symplectic structure defined by a closed weakly exact 2-form $\sigma$ on $M$ whose lift to the universal cover of $M$ admits a…
The Rabinowitz-Floer homology of a Liouville domain W is the Floer homology of the free period Hamiltonian action functional associated to a Hamiltonian whose zero energy level is the boundary of W. It has been introduced by K. Cieliebak…
The Rabinowitz-Floer homology groups $RFH_*(M,W)$ are associated to an exact embedding of a contact manifold $(M,\xi)$ into a symplectic manifold $(W,\omega)$. They depend only on the bounded component $V$ of $W\setminus M$. We construct a…
In this paper we prove a generalisation of Schlenk's theorem about the existence of contractible periodic Reeb orbits on stable, displaceable hypersurfaces in symplectically aspherical, geometrically bounded, symplectic manifolds, to a…
Rabinowitz Floer homology is the semi-infinite dimensional Morse homology associated to the Rabinowitz action functional used in the pioneering work of Rabinowitz. Gradient flow lines are solutions of a vortex-like equation. In this survey…
We study the dynamics and symplectic topology of energy hypersurfaces of mechanical Hamiltonians on twisted cotangent bundles. We pay particular attention to periodic orbits, displaceability, stability and the contact type property, and the…
We define the $S^1$-equivariant Rabinowitz-Floer homology of a bounding contact hypersurface $\Sigma$ in an exact symplectic manifold, and show by a geometric argument that it vanishes if $\Sigma$ is displaceable. In the appendix we…
We compute the Rabinowitz Floer homology for a class of non-compact hyperboloids $\Sigma\simeq S^{n+k-1}\times\mathbb{R}^{n-k}$. Using an embedding of a compact sphere $\Sigma_0\simeq S^{2k-1}$ into the hypersurface $\Sigma$, we construct a…
Rabinowitz Floer homology has been investigated on a submanifold of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study…
We use Hamiltonian Floer theory to recover and generalize a classic rigidity theorem of Ekelend and Lasry. That theorem can be rephrased as an assertion about the existence of multiple closed Reeb orbits for certain tight contact forms on…
In this paper, we extend Rabinowitz Floer homology theory which has been established and extensively studied for hypersurfaces to coisotropic submanifolds of higher codimension. With this generalized version of Rabinowitz Floer homology…
In this paper, we construct the Rabinowitz-Floer homology for the coupled Dirac system \begin{equation*} \left\{ \begin{aligned} Du=\frac{\partial H}{\partial v}(x,u,v)\hspace{4mm} {\rm on} \hspace{2mm}M,\\ Dv=\frac{\partial H}{\partial…
Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set,…
We show that the category of linearly topologized vector spaces over discrete fields constitutes the correct framework for algebraic structures on Floer homologies with field coefficients. Our case in point is the Poincar\'e duality theorem…
We study the following rigidity problem in symplectic geometry:can one displace a Lagrangian submanifold from a hypersurface? We relate this to the Arnold Chord Conjecture, and introduce a refined question about the existence of relative…