Morse-Novikov cohomology on foliated manifolds

DOI10.1016/j.difgeo.2023.102100arXiv2202.04508MaRDI QIDQ6192125

M.D. Shariful Islam

Publication date: 11 March 2024

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.04508

zbMATH Keywords

cohomologyfoliationhomotopy invariancePoincaré dualityHodge theory

Mathematics Subject Classification ID

Hodge theory in global analysis (58A14) Foliations (differential geometric aspects) (53C12) Foliations in differential topology; geometric theory (57R30)

Cites Work

• Basic Morse-Novikov cohomology for foliations
• Modified differentials and basic cohomology for Riemannian foliations
• Morse-Novikov cohomology of almost nonnegatively curved manifolds
• Morse-Novikov cohomology of locally conformally Kähler manifolds
• Locally conformal symplectic manifolds
• Supersymmetry and Morse theory
• Hodge decomposition along the leaves of Riemannian foliation
• Les variétés de Poisson et leurs algèbres de Lie associees
• Generalized Hopf manifolds
• Essential self-adjointness of powers of generators of hyperbolic equations
• Long time behavior of leafwise heat flow for Riemannian foliations
• Harmonic Integrals on Foliated Manifolds
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Novikov type inequalities for differential forms with non-isolated zeros
• A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
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