Related papers: Geometric Cycles in Floer Theory

We prove that Floer cohomology of cyclic Lagrangian correspondences is invariant under transverse and embedded composition of Lagrangians under a general set of assumptions. In the Corrigendum, we introduce an additional assumption of…

In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present formulation is closer in spirit to the usual…

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle of a compact orientable manifold M. The first result is a new uniform estimate for the solutions of the Floer equation,…

We resolve the long-standing problem of constructing the action of the operad of framed (stable) genus-$0$ curves on Hamiltonian Floer theory; this operad is equivalent to the framed $E_2$ operad. We formulate the construction in the…

Assume $M$ to be $\mathbb R^2$ or a closed surface of genus $g \geq 1$ and $\omega$ a symplectic form on $M$. Let $\varphi: M \to M$ be a symplectomorphism with hyperbolic fixed point $x$ and transversely intersecting stable and unstable…

The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for…

We introduce a new notion of persistence modules endowed with operators. It encapsulates the additional structure on Floer-type persistence modules coming from the intersection product with classes in the ambient (quantum) homology, along…

We establish a criterion on wrapped Floer homology of an exact Lagrangian sub- manifold in a Liouville domain, which ensures the almost-existence of Hamiltonian chords near a given energy level. To this purpose we introduce a relative…

In $n$-dimensional classical field theory one studies maps from $n$-dimensional manifolds in such a way that classical mechanics is recovered for $n=1$. In previous papers we have shown that the standard polysymplectic framework in which…

Following \cite{citeSavelyevVirtualMorsetheoryon$Omega$Ham$(Momega)$.}, we develop here a connection between Morse theory for the (positive) Hofer length functional $L: \Omega \text {Ham}(M, \omega) \to \mathbb{R}$, with Gromov-Witten/Floer…

In this paper we show how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures in Hamiltonian Floer theory. Using the SFT of Hamiltonian mapping tori we…

In this survey paper, we will collate various different ideas and thoughts regarding equivariant operations on quantum cohomology (and some in more general Floer theory) for a symplectic manifold. We will discuss a general notion of…

We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations…

We show how Rabinowitz Floer homology can be seen as a standard Floer homology for fixed period Hamiltonian orbits on an extended phase space.

In the setting of symplectic manifolds which are convex at infinity, we use a version of the Aleksandrov maximum principle to derive uniform estimates for Floer solutions that are valid for a wider class of Hamiltonians and almost complex…

In this paper, Floer homology for Lagrangian submanifolds in an open symplectic manifold given as the complement of a smooth divisor is discussed. The main new feature of this construction is that we do not make any assumption on positivity…

Hamiltonian Floer theory plays an important role for finding periodic solutions of Hamilton's equation, which can be seen as a generalization of Newton's equation. Generalizing Newton's equation to Laplace's equation with non-linearity, we…

We study possible configurations of singular points occuring on general algebraic curves in $\mathbb{C}P^2$ via Floer theory. To achieve this, we describe a general formula for the $H_{1}$-action on the knot Floer complex of the…

We give a new proof of the Morse Homology Theorem by constructing a chain complex associated to a Morse-Bott-Smale function that reduces to the Morse-Smale-Witten chain complex when the function is Morse-Smale and to the chain complex of…

In this article we consider two classical problems in Quantum Mechanics, namely the 'particle on a ring' and the 'particle in a box' from the viewpoint of symplectic topology. Interpreting the solutions of the corresponding time independent…