Morse–Conley–Floer homology

DOI10.1142/S1793525314500174zbMath1350.37018arXiv1305.4074OpenAlexW2157375645MaRDI QIDQ2874671

Thomas O. Rot, Robert C. A. M. VanderVorst

Publication date: 8 August 2014

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4074

zbMATH Keywords

Lyapunov functionsConley index theoryMorse homology

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Dynamics induced by flows and semiflows (37C10) Index theory for dynamical systems, Morse-Conley indices (37B30) Other homology theories in algebraic topology (55N35)

Related Items

The Triangulation of Manifolds: Topology, Gauge Theory, and History, The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology, Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces, Connected components of the space of proper gradient vector fields, Functoriality and duality in Morse-Conley-Floer homology

Cites Work

• Floer homology of cotangent bundles and the loop product
• Witten's complex and infinite dimensional Morse theory
• Continuation to gradient flows
• Morse homology and degenerate Morse inequalities
• Symplectic fixed points and holomorphic spheres
• The Morse-Witten complex via dynamical systems
• On gradient dynamical systems
• Lyapunov functions and isolating blocks
• Lyapunov maps, simplicial complexes and the Stone functor
• Morse Theory, the Conley Index and Floer Homology
• Mappings and homological properties in the Conley index theory
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• A cohomological Conley index in Hilbert spaces and applications to strongly indefinite problems