#### Vol. 298, No. 1, 2019

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Equivariant formality of Hamiltonian transversely symplectic foliations

### Yi Lin and Xiangdong Yang

Vol. 298 (2019), No. 1, 59–82
DOI: 10.2140/pjm.2019.298.59
##### 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.

##### Keywords
transversely symplectic foliations, Hamiltonian actions, equivariant formality
Primary: 57S25
Secondary: 57R91