A note on the basic Lichnerowicz cohomology of transversally locally conformally K\"{a}hlerian foliations
Cristian Ida
TL;DR
This paper extends the theory of basic Lichnerowicz cohomology to transversally locally conformally Kählerian foliations and explores its connections with basic Bott-Chern and Dolbeault cohomologies.
Contribution
It generalizes the basic Lichnerowicz cohomology framework and investigates its relationship with other basic cohomologies in the context of foliations.
Findings
Established a generalized form of basic Lichnerowicz cohomology.
Analyzed the relation with basic Bott-Chern cohomology.
Explored the connection with 0-th basic Dolbeault cohomology.
Abstract
In this paper we generalize the basic Lichnerowicz cohomology on transversally locally conformally K\"{a}hlerian foliations and we study its relation with basic Bott-Chern cohomology and --th basic Dolbeault cohomology with values in the associated foliated weight bundle.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology