Cyclic Homology of Fukaya Categories and the Linearized Contact Homology

Details Cyclic Homology of Fukaya Categories and the Linearized Contact Homology Cyclic Homology of Fukaya Categories and the Linearized Contact Homology

2012-01-24

arxiv.org/abs/1201.4907v2

Mathematics

Symplectic Geometry

34 pages, 5 figures

Scientific paper

Let $M$ be an exact symplectic manifold with contact type boundary such that $c_1(M)=0$. In this paper we show that the cyclic cohomology of the Fukaya category of $M$ has the structure of an involutive Lie bialgebra. Inspired by a work of Cieliebak-Latschev we show that there is a Lie bialgebra homomorphism from the linearized contact homology of $M$ to the cyclic cohomology of the Fukaya category. Our study is also motivated by string topology and 2-dimensional topological conformal field theory.

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