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Morse-Novikov cohomology on foliated manifolds.
- Source :
-
Differential Geometry & its Applications . Apr2024, Vol. 93, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential d ω = d + ω ∧ , where ω is a closed 1-form. We study Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy invariance and then extend it to more general type of forms on a Riemannian foliation. We study the Laplacian and Hodge decompositions for the corresponding differential operators on reduced leafwise Morse-Novikov complexes. In the case of Riemannian foliations, we prove that the reduced leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and Poincaré duality. The resulting isomorphisms yield a Hodge diamond structure for leafwise Morse-Novikov cohomology. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09262245
- Volume :
- 93
- Database :
- Academic Search Index
- Journal :
- Differential Geometry & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 175832840
- Full Text :
- https://doi.org/10.1016/j.difgeo.2023.102100