Related papers: A variational approach to Givental's nonlinear Mas…
We define a new variant of Rabinowitz Floer homology that is particularly well suited to studying the growth rate of leaf-wise intersections. We prove that for closed manifolds $M$ whose loop space is "complicated", if $\Sigma$ is 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…
This paper establishes the orderability of contact manifolds which are quotients of fillable contact manifolds under finite group actions compatible with the filling, the prototypical example being $\mathbb{R}P^{2n-1}$ as the quotient of…
In this article we explain how critical points of a particular perturbation of the Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type. This is used to derive existence and…
We build homogeneous quasi-morphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Givental's nonlinear Maslov index and a contact reduction…
Givental's non-linear Maslov index, constructed in 1990, is a quasimorphism on the universal cover of the identity component of the contactomorphism group of real projective space. This invariant was used by several authors to prove contact…
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…
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…
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…
In this paper, we construct a Rabinowitz-Floer type homology for a class of non-linear problems having a \emph{starshaped} potential; we consider some equivariant cases as well. We give an explicit computation of the homology and we apply…
In this article, we focus on the invariance property of Morse homology on noncompact manifolds. We expect to apply outcomes of this article to several types of Floer homology, thus we define Morse homology purely axiomatically and…
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…
We prove that if a contact manifold admits an exact filling then every local contactomorphism isotopic to the identity admits a translated point in the interior of its support, in the sense of Sandon [San11b]. In addition we prove that if…
In this paper we find that the asymptotic nonlinear Maslov index defined on the universal cover of the group of all contact Hamiltonian diffeomorphisms of the standard 2n-1 dimensional contact sphere is a quasimorphism. Then we show our…
In this note the interrelations between several natural morphisms on the $\pi_1$ of groups of Hamiltonian diffeomorphisms are investigated. As an application, the equality of the (non-linear) Maslov index of loops of quantomorphisms of…
This paper represents a first step towards the extension of the definition of Rabinowitz Floer homology to non-compact energy hypersurfaces in exact symplectic manifolds. More concretely, we study under which conditions it is possible to…
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…
In this paper we investigate the properties of a semi-linear problem on a spin manifold involving the Dirac operator, through the construction of Rabinowitz-Floer homology groups. We give several existence results for sub-critical and…
We prove a generalized version of the Morse index theorem for geodesics endowed with a non positive definite metric tensor (semi-Riemannian manifolds). We apply the result to obtain lower estimates on the number of geodesics joining two…
In this article we study Rabinowitz Floer Homology for several interaction particles. In general Rabinowitz action functional is invariant under simultaneous time translation for all particles but not invariant if the times of each particle…