The Frolicher-type inequalities of foliations
Pawe{\l} Ra\'zny
TL;DR
This paper extends Frolicher-type inequalities to transversely holomorphic and symplectic foliations, providing tools to analyze their geometric structures and potential for transverse Kähler properties.
Contribution
It adapts Frolicher-type inequalities to foliations and orbifolds, linking them to dd'-lemmas and transverse Kähler conditions.
Findings
Frolicher-type inequalities are established for transversely holomorphic foliations.
These inequalities help determine the existence of transverse Kähler structures.
Results are applicable to orbifolds as well.
Abstract
The purpose of this article is to adapt the Frolicher-type inequality to the case of transversely holomorphic and transversely symplectic foliations. These inequalities can be used to e.g. determine whether a given foliation can be made transversely Kahler (due to their relations to various dd'-lemmas). Our main results can be also stated for orbifolds as we point out in section 5 of this paper.
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