Basic Morse-Novikov cohomology for foliations
Liviu Ornea, Vladimir Slesar
TL;DR
This paper establishes conditions under which Morse-Novikov cohomology vanishes for Riemannian foliations, extending classical results and providing new examples and applications in locally conformally symplectic and Kähler foliations.
Contribution
It introduces a Bochner technique for twisted cohomological complexes on foliations and generalizes vanishing results from closed manifolds to foliated settings.
Findings
Vanishing conditions for Morse-Novikov cohomology on Riemannian foliations
Extension of classical vanishing results to foliated manifolds
Examples and applications in l.c.s. and l.c.K. foliations
Abstract
In this paper we find sufficient conditions for the vanishing of the Morse-Novikov cohomology on Riemannian foliations. We work out a Bochner technique for twisted cohomological complexes, obtaining corresponding vanishing results. Also, we generalize for our setting vanishing results from the case of closed Riemannian manifolds. Several examples are presented, along with applications in the context of l.c.s. and l.c.K. foliations.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Topological and Geometric Data Analysis · Geometry and complex manifolds