1201.4907 (Xiaojun Chen et al.)

Cyclic Homology of Fukaya Categories and the Linearized Contact Homology    [PDF]

Xiaojun Chen, Hai-Long Her, Shanzhong Sun

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.

View original: http://arxiv.org/abs/1201.4907