Morse-Bott homology

DOI10.1090/S0002-9947-10-05073-7zbMath1226.57038arXivmath/0612316OpenAlexW2042479246MaRDI QIDQ3581127

Hurtubise, David E., Augustin Banyaga

Publication date: 16 August 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612316

zbMATH Keywords

critical manifoldsfibered productsMorse-Bott-Smale functionsThe Morse-Bott-Smale chain complex and its homology

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Floer homology (57R58) Critical points and critical submanifolds in differential topology (57R70) Algebraic topology on manifolds and differential topology (57R19) Morse-Smale systems (37D15)

Related Items (9)

On Morse-Smale-Witten type cohomologies for orbifolds ⋮ Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization ⋮ Cascades and perturbed Morse-Bott functions ⋮ Morse theory for Lagrange multipliers and adiabatic limits ⋮ MULTICOMPLEXES AND SPECTRAL SEQUENCES ⋮ 2-Morse theory and algebra of the infrared ⋮ Axiomatic \(S^1\) Morse-Bott theory ⋮ Optimal Łojasiewicz-Simon inequalities and Morse-Bott Yang-Mills energy functions ⋮ Orbifold Morse–Smale–Witten complexes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Morse homology
• Triangulation and general position of PL diagrams
• A general Fredholm theory. II: Implicit function theorems
• Filling Riemannian manifolds
• Morse theory for Lagrangian intersections
• Acyclic models for multicomplexes
• On the equivalence of multiplicative structures in Floer homology and quantum homology
• Coherent orientations for periodic orbit problems in symplectic geometry
• Compactness results in symplectic field theory
• The flow category of the action functional on \({\mathcal L}G_{N,N+K} (\mathbb{C})\)
• Gradient flows of Morse-Bott functions
• Symplectic fixed points and holomorphic spheres
• An instanton-invariant for 3-manifolds
• Torus actions on symplectic manifolds
• Bott-type symplectic Floer cohomology and its multiplication structures
• Floer homology of connected sum of homology 3-spheres
• Equivariant Floer theory and gluing Donaldson polynomials
• A general Fredholm theory. I: A splicing-based differential geometry
• Lagrangian intersections and the Serre spectral sequence
• The Morse-Witten complex via dynamical systems
• A proof of the Morse-Bott lemma.
• Nondegenerate critical manifolds
• Applications of the Theory of Morse to Symmetric Spaces
• The Morse–Bott inequalities via a dynamical systems approach
• Transversality and the inverse image of a submanifold with corners.
• Convexity and Commuting Hamiltonians
• The Yang-Mills equations over Riemann surfaces
• MULTICOMPLEXES AND SPECTRAL SEQUENCES
• Finite volume flows and Morse theory

This page was built for publication: Morse-Bott homology