Equivariant formality of transversely symplectic foliations and Frobenius manifolds

Abstract

Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation which satisfies the transverse hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic $d\delta$-lemma in this setting. As an application, we show that if the foliation is also Riemannian, then there exists a natural formal Frobenius manifold structure on the equivariant basic cohomology of the foliation.

arXiv comment26 pages, no figures, comments welcome

References in corpus (7)

• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• Formality of canonical symplectic complexes and Frobenius manifolds
• A remark on the Hard Lefschetz Theorem for Kähler orbifolds
• Cohomological tautness for Riemannian foliations
• A non-Sasakian Lefschetz K-contact manifold of Tievsky type
• Convexity properties of presymplectic moment maps
• Formal Frobenius manifold structure on equivariant cohomology

Cited by in corpus (1)

• Basic Kirwan injectivity and its applications