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 dδ-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
Authors
Yi Lin
Department of Mathematical Sciences
Georgia Southern University
Statesboro, GA
United States
Xiangdong Yang
Department of Mathematics
Chongqing University
Chongqing
China