Witten's complex and infinite-dimensional Morse theory

Andreas Floer

Type: Article

Publication Date: 1989-01-01

Citations: 268

DOI: https://doi.org/10.4310/jdg/1214443291

Abstract

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.

Locations

Journal of Differential Geometry - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Morse Theory of Gradient Flows, Concavity and Complexity on Manifolds with Boundary	2011	Gabriel Katz
+	LECTURES ON THE MORSE COMPLEX FOR INFINITE-DIMENSIONAL MANIFOLDS	2005	Alberto Abbondandolo Pietro Majer
+	Morse Theory and Floer Homology	2002	Jürgen Jost
+	Introduction to Morse theory and Morse homology	2021	Julian David Espinel Leal
+	Homología de Morse en variedades compactas	2011	Carlos A. Arango
+ PDF Chat	The Morse–Witten complex via dynamical systems	2005	Joa Weber
+	The Trajectory Spaces	1993	Matthias Schwarz
+	The moduli space of gradient flow lines and Morse homology	2020	Urs Frauenfelder Robert D. Nicholls
+	Witten deformations, geometry and dynamics	2018	Leonardo Masci
+	Flows in Flatland: A Romance of Few Dimensions	2015	Gabriel Katz
+	Flows in Flatland: A Romance of Few Dimensions	2015	Gabriel Katz
+	Morse homology for the Hamiltonian action in cotangent bundles	2022	Asselle L. Starostka M
+	Floer Homology: Spaces of Trajectories	2013	Michèle Audin Mihai Damian
+	A Morse complex for infinite dimensional manifolds—part I	2004	Alberto Abbondandolo Pietro Majer
+	On the dynamics of transversely holomorphic flows on closed 3-manifolds	2009	Jaeyoo Choy Hahng-Yun Chu
+	A short course on Witten Helffer-Sjöstrand theory	2001	Dan Burghelea
+	Orbifold Morse-Smale-Witten complex	2011	Cheol-Hyun Cho Hansol Hong
+	Morse-Bott homology	2010	Augustin Banyaga David Hurtubise
+	Gradient flows of Morse-Bott functions	2000	Janko Latschev
+	C^0-topology in Morse theory	2003	Andrei Pajitnov

Works That Cite This (254)

Action	Title	Year	Authors
+	Floer-Novikov fundamental group and small flux symplectic isotopies	2021	Jean-François Barraud Agnès Gadbled
+	Quantum theories and geometric topology: A chapter in physical mathematics	2014	Kishore Marathe
+ PDF Chat	Floer theory and its topological applications	2015	Ciprian Manolescu
+ PDF Chat	A brief survey of the spectral numbers in floer homology	2020	Jelena Katić Darko Milinković Jovana Nikolić
+	Poincaré-Birkhoff Theorems in random dynamics	2016	Álvaro Pelayo Fraydoun Rezakhanlou
+ PDF Chat	Lagrangian intersections and the Serre spectral sequence	2007	Jean-François J.-F. B. Barraud Octav Cornea
+	Cellular Legendrian contact homology for surfaces, part III	2019	Daniel Rutherford Michael G. Sullivan
+ PDF Chat	Bounding Lagrangian widths via geodesic paths	2014	Matthew Strom Borman Mark McLean
+	Quantum and Floer cohomology have the same ring structure	1994	Sergey Piunikhin
+	Applications of the theory of Floer to symmetric spaces	2021	Hanwool Bae Chi Hong Chow Naichung Conan Leung

Works Cited by This (9)

Action	Title	Year	Authors
+	Isolated Invariant Sets and the Morse Index	1978	Charles C. Conley
+ PDF Chat	Morse theory for Lagrangian intersections	1988	Andreas Floer
+	Lectures on the H-Cobordism Theorem	1965	John Milnor
+ PDF Chat	Morse decompositions and connection matrices	1988	Richard Moeckel
+	On Gradient Dynamical Systems	1961	Stephen T. Smale
+ PDF Chat	Morse inequalities for a dynamical system	1960	Stephen T. Smale
+	The unregularized gradient flow of the symplectic action	1988	Andreas Floer
+	Characteristic Classes. (AM-76)	1974	John Milnor James Stasheff
+	Homology	1966	Edwin H. Spanier