# WITTEN'S COMPLEX AND INFINITE DIMENSIONAL MORSE THEORY

@article{Floer1989WITTENSCA, title={WITTEN'S COMPLEX AND INFINITE DIMENSIONAL MORSE THEORY}, author={Andreas Floer}, journal={Journal of Differential Geometry}, year={1989}, volume={30}, pages={207-221} }

We investigate the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space. The results are applied to an infinite dimensional problem involving the symplectίc action function.

## 302 Citations

Morse-Bott theory and equivariant cohomology

- Mathematics
- 1995

Critical points of functions and gradient lines between them form a cornerstone of physical thinking. In Morse theory the topology of a manifold is investigated in terms of these notions with equally…

Unstable geodesics and topological field theory

- Mathematics, Physics
- 1994

A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the Becchi–Rouet–Stora–Tyutin cohomology realizing the physical Hilbert space and the…

The cup-product on the Thom-Smale-Witten complex, and Floer cohomology

- Mathematics
- 1995

Let M be a finite dimensional smooth manifold, f a C2 Morse function on M satisfying the Palais-Smale condition

Morse Theory without Non-Degeneracy

- Mathematics
- 2019

We describe an extension of Morse theory to smooth functions on compact Riemannian manifolds, without any nondegeneracy assumptions except that the critical locus must have only finitely many…

LECTURES ON THE MORSE COMPLEX FOR INFINITE-DIMENSIONAL MANIFOLDS

- Mathematics
- 2006

After reviewing some classical results about hyperbolic dynamics in a Banach setting, we describe the Morse complex for gradient-like flows on an infinite-dimensional Banach manifold M, under the…

The Conley index, gauge theory, and triangulations

- Mathematics
- 2013

This is an expository paper about Seiberg–Witten Floer stable homotopy types.We outline their construction, which is based on the Conley index and finite-dimensional approximation. We then describe…

Reidemeister torsion and integrable Hamiltonian systems

- Mathematics
- 1998

In this paper, we compute the Reidemeister torsion of an isoenergetic surface for the integrable Hamiltonian system on the 4-dimensional symplectic manifold. We use the spectral sequence defined by…

Floer Homology and the Heat Flow

- Mathematics
- 2006

Abstract.We study the heat flow in the loop space of a closed Riemannian manifold M as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the…

ESI The Erwin

- Philosophy
- 1998

In this paper we compute the Reidemeister torsion of a isoenergetic surface for the integrable Hamiltonian system on the four-dimensional symplectic manifold. We use the spectral sequence defined by…

Exponential Convergence to Non-degenerate Reeb Chords

- Mathematics
- 2021

Exponential convergence type results are proved for holomorphic curves in the symplectization of a contact manifold $Y$ with boundary on a Legendrian cylinder. The results are proven in all…

## References

SHOWING 1-10 OF 10 REFERENCES

Isolated Invariant Sets and the Morse Index

- Mathematics
- 1978

On stable properties of the solution set of an ordinary differential equation Elementary properties of flows The Morse index Continuation Bibliography.

Supersymmetry and Morse theory

- Physics
- 1982

It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian. Some of the implications of modern ideas in mathematics for…

Morse decompositions and connection matrices

- MathematicsErgodic Theory and Dynamical Systems
- 1988

Abstract This paper surveys the work of Charles Conley and his students on Morse decompositions for flows on compact metric spaces, as well as the more recent development of the connection matrix…

Algebraic Topology

- Mathematics

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.

The unregularized gradient flow of the symplectic action

- Mathematics
- 1988

The symplectic action can be defined on the space of smooth paths in a symplectic manifold P which join two Lagrangian submanifolds of P. To pursue a new approach to the variational theory of this…

Morse theory for Lagrangian intersections

- Mathematics
- 1988

Soit P une variete symplectique compacte et soit L⊂P une sous-variete lagrangienne avec π 2 (P,L)=0. Pour un diffeomorphisme exact φ de P avec la propriete que φ(L) coupe L transversalement, on…

On Gradient Dynamical Systems

- Mathematics
- 1961

We consider in this paper a Co vector field X on a Co compact manifold Mn (&M, the boundary of M, may be empty or not) satisfying the following conditions: (1) At each singular point /8 of X, there…

Sur une partition en cellules associee a unefonction sur une variete

- C.R. Acad. Sci. Paris 228
- 1949

Sjόstrand, Puits multiples en mechanique semiclassique IV; etude du complexe de Witten, Comm

- Partial Differential Equations
- 1985