Equivariant Formality of Transversely Symplectic Foliations and Frobenius Manifolds

Yi Lin, Xiangdong Yang

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Abstract

Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation whose basic cohomology satisfies the Hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic dδ-lemma in this setting. As an application, we show that there exists a natural Frobenius manifold structure on the equivariant basic cohomology of the given foliation. In particular, this result provides a class of new examples of dGBV-algebras whose cohomology carries a Frobenius manifold structure.

Original languageAmerican English
JournalarXiv Repository
StatePublished - Sep 3 2016

Disciplines

  • Education
  • Mathematics

Keywords

  • Equivariant Formality
  • Frobenius Manifolds
  • Transversely Symplectic Foliations

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