## Figures from this paper

## 10 Citations

### The Poincaré-Hopf theorem for relative braid classes

- Mathematics
- 2012

This paper studies the existence and multiplicity of closed integral curves of smooth vector fields on the closed 2-disc $${ \mathbb {D}^2}$$D2 in the complement of a suitable geometric braid…

### Braid stability and the Hofer metric

- Mathematics
- 2021

In this article we show that the braid type of a set of 1periodic orbits of a non-degenerate Hamiltonian diffeomorphism on a surface is stable under perturbations which are sufficiently small with…

### FLOER HOMOLOGY, RELATIVE BRAID CLASSES, AND LOW DIMENSIONAL DYNAMICS

- Mathematics
- 2010

Floer homology is a powerful variational technique used in Symplectic Geometry to derive a Morse type theory for the Hamiltonian action functional. In two and three dimensional dynamics the…

### Hamiltonian Floer theory on surfaces

- Mathematics
- 2021

We develop connections between the qualitative dynamics of Hamiltonian isotopies on a surface Σ and their chain-level Floer theory using ideas drawn from Hofer-Wysocki-Zehnder’s theory of finite…

### Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points

- Mathematics
- 2022

To make progress towards better computability of Morse-Floer homology, and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative index of equilibria.…

### A symplectic proof of a theorem of Franks

- MathematicsCompositio Mathematica
- 2012

Abstract A celebrated theorem in two-dimensional dynamics due to John Franks asserts that every area-preserving homeomorphism of the sphere has either two or infinitely many periodic points. In this…

### Contact homology of orbit complements and implied existence

- Mathematics
- 2011

For Reeb vector fields on closed 3-manifolds, cylindrical contact homology is used to show that the existence of a set of closed Reeb orbit with certain knotting/linking properties implies the…

### TOPOLOGICAL AND DYNAMICAL METHODS FOR DATA ANALYSIS

- Mathematics
- 2018

My interests lie in the development of theories, algorithms and software for the analysis of nonlinear data and systems. My recent work is in Conley index theory, where I developed both a categorical…

### Braid Floer Homology on Surfaces

- Mathematics
- 2016

The Arnold Conjecture gives the existence of 1-periodic solutions of a nondegenerate Hamiltonian system on a compact symplectic manifold. This Conjecture is proved for aspherical manifolds with the…

## References

SHOWING 1-10 OF 55 REFERENCES

### A survey of Floer homology for manifolds with contact type boundary or symplectic homology

- MathematicsEnsaios Matemáticos
- 2004

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…

### J-Holomorphic Curves and Symplectic Topology

- Mathematics
- 2004

The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was…

### Morse theory on spaces of braids and Lagrangian dynamics

- Mathematics
- 2001

Abstract.In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the…

### Morse theory, the Conley index and Floer homology

- Mathematics
- 1990

In 1965 Arnold [1] conjectured that the number of fixed points of an exact symplectic diffeomorphism on a symplectic manifold M can be estimated below by the sum of the Betti numbers provided that…

### Symplectic Floer homology of area-preserving surface diffeomorphisms

- Mathematics
- 2009

The symplectic Floer homology HF_*(f) of a symplectomorphism f:S->S encodes data about the fixed points of f using counts of holomorphic cylinders in R x M_f, where M_f is the mapping torus of f. We…

### Functors and Computations in Floer Homology with Applications, I

- Mathematics
- 1999

Abstract. This paper is concerned with Floer cohomology of manifolds with contact type boundary. In this case, there is no conjecture on this ring, as opposed to the compact case, where it is…

### Symplectic Invariants and Hamiltonian Dynamics

- Mathematics
- 1994

The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: sympletic topology. Surprising rigidity phenomena…

### Braids, Links, and Mapping Class Groups.

- Mathematics
- 1975

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with…

### Morse theory for periodic solutions of hamiltonian systems and the maslov index

- Mathematics
- 1992

In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the…

### Hamiltonian systems with three or more degrees of freedom

- Mathematics
- 1999

Preface. List of Participants. Lectures. Contributions. List of Authors. Subject Index. Lectures. Inflection points, extatic points and curve shortening S. Angenent. Topologically necessary…