MORSE–NOVIKOV CRITICAL POINT THEORY, COHN LOCALIZATION AND DIRICHLET UNITS

DOI10.1142/S0219199799000171zbMath0964.57030arXivmath/9911157MaRDI QIDQ4514928

Michael S. Farber

Publication date: 14 November 2000

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911157

zbMATH Keywords

Morse theorycritical pointsMorse indexmanifolds with cornersNovikov inequalitiesflat vector bundlesclosed \(1\)-formschain collapseNovikov chain complex

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Global differential geometry (53C99) Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (57Q10) Critical points and critical submanifolds in differential topology (57R70)

Related Items (2)

On the Whitehead group of Novikov rings associated to irrational homomorphisms ⋮ Controlled connectivity of closed \(1\)-forms

Cites Work

• Exactness of the Novikov inequalities
• Rationality and exponential growth properties of the boundary operators in the Novikov complex
• On the Novikov complex for rational Morse forms
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Un problème de disjonction par isotopie symplectique dans un fibré cotangent
• Dirichlet units and critical points of closed 1-forms
• Novikov type inequalities for differential forms with non-isolated zeros

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