Novikov homology, twisted Alexander polynomials, and Thurston cones

DOI10.1090/S1061-0022-07-00975-2zbMath1137.57017arXivmath/0406498OpenAlexW2963720485MaRDI QIDQ5440784

Andrei V. Pajitnov

Publication date: 5 February 2008

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406498

zbMATH Keywords

twisted Alexander polynomialThurston normMorse formNovikov cohomology

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Algebraic topology on manifolds and differential topology (57R19)

Related Items

A Survey of the Thurston Norm ⋮ Twisted Novikov homology of complex hypersurface complements ⋮ Twisted Alexander polynomials of twist knots for nonabelian representations ⋮ ALEXANDER–LIN TWISTED POLYNOMIALS ⋮ Novikov homology, jump loci and Massey products ⋮ Closed 1-forms and twisted cohomology

Cites Work

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• Modules over some localizations of the ring of Laurent polynomials
• Supersymmetry and Morse theory
• Heegaard splitting for sutured manifolds and Murasugi sum
• Algebraic K-theory of generalized free products. II
• On handle number of Seifert surfaces in \(S^ 3\)
• On the asymptotics of Morse numbers of finite covers of manifolds
• Twisted Alexander polynomial for finitely presentable groups
• One-parameter fixed-point theory and gradient flows of closed 1-forms
• Reidemeister torsion, twisted Alexander polynomial and fibered knots
• Existence of nonsingular closed 1-forms in a de Rham cohomology class
• On the Novikov complex for rational Morse forms
• Surgery on the Novikov complex
• Twisted Alexander polynomial and Reidemeister torsion
• Twisted Novikov homology and circle-valued Morse theory for knots and links
• The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology1
• On the Homotopy Type of Certain Two-Dimensional Complexes
• Gradient flows of closed 1-forms and their closed orbits
• Knots
• The Whitehead group of the Novikov ring
• Representations of knot groups and twisted Alexander polynomials
• A norm for the cohomology of 2-complexes