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 language | American English |
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Journal | arXiv Repository |
State | Published - Sep 3 2016 |
Disciplines
- Education
- Mathematics
Keywords
- Equivariant Formality
- Frobenius Manifolds
- Transversely Symplectic Foliations