Morse-Conley-Floer Homology

Abstract

For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue of the Conley index and the Morse-Conley relations. The approach will be referred to as Morse-Conley-Floer homology.

References in corpus (5)

• Functors and Computations in Floer homology with Applications Part II
• The Morse-Witten complex via dynamical systems
• A Morse complex for infinite dimensional manifolds - Part I
• Functoriality in Morse theory on closed manifolds
• The Poincaré-Hopf Theorem for relative braid classes

Cited by in corpus (4)

• Improving the Utility of Differentially Private Clustering through Dynamical Processing
• Homological Description of the Quantum Adiabatic Evolution With a View Toward Quantum Computations
• Symplectic monodromy at radius zero and equimultiplicity of $\mu$-constant families
• Functoriality and duality in Morse-Conley-Floer homology