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

Mathematical Subject Classification 2010

Primary: 57S25

Secondary: 57R91

Milestones

Received: 18 July 2017

Revised: 3 August 2018

Accepted: 6 August 2018

Published: 2 February 2019