COMBINATORIAL NOVIKOV–MORSE THEORY

DOI10.1142/S0129167X02001265zbMath1052.57053MaRDI QIDQ4807402

Robin Forman

Publication date: 18 May 2003

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Morse inequalitiesReidemeister torsionCW-complexescombinatorial differential formsNovikov-Morse theory

Mathematics Subject Classification ID

General topology of complexes (57Q05) Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (57Q10) Critical points and critical submanifolds in differential topology (57R70)

Related Items (7)

Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet theorem ⋮ The main theorem of discrete Morse theory for Morse matchings with finitely many rays ⋮ Discrete field theory: symmetries and conservation laws ⋮ Creating semiflows on simplicial complexes from combinatorial vector fields ⋮ Relation between combinatorial Ricci curvature and Lin-Lu-Yau's Ricci curvature on cell complexes ⋮ Emergent time, cosmological constant and boundary dimension at infinity in combinatorial quantum gravity ⋮ Diffusion in multi-dimensional solids using Forman's combinatorial differential forms

Cites Work

• Novikov numbers
• Homological identities for closed orbits
• Exactness of the Novikov inequalities
• Structure of level surfaces of a Morse form
• Supersymmetry and Morse theory
• Combinatorial vector fields and dynamical systems
• Witten-Morse theory for cell complexes
• Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds
• A combinatorial decomposition of simplicial complexes
• Morse theory for cell complexes
• Existence of nonsingular closed 1-forms in a de Rham cohomology class
• A smooth counterexample to the Seifert conjecture
• The Seiberg-Witten and Gromov invariants
• Surgery on the Novikov complex
• On the minimal sets of non-singular vector fields
• R-torsion and the Laplacian on Riemannian manifolds
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Whitehead torsion

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