# Nikita Markarian’s mathblog

## Manifoldic homology and Chern-Simons formalism

Posted in Mathematics by nikitamarkarian on July 30, 2011

My preprint arXiv:1106.5352v1 is mostly inspired by the perfect explanation of Damien Calaque of the Kevin Costello’s project. Given a $e_n$-algebra $A$ and a compact parallelized $n$-manifold without borders $M$ a morphism from homology of the Lie algebra $L(A)$ associated with $A$ to some manifoldic homology is constructed in the preprint. I guess that for a proper $A$ this morphism gives perturbative Chern-Simons invariants of $M$ and that this construction is closely connected with the Costello’s approach. Some comments are under the cut. (more…)

The universal enveloping $e_n$-algebra is a functor from the category of homotopy Lie algebras over $Q$ to the category of algebras over the operad of rational chains of the operad of little $n-$discs. For $n=1$ one get (the derived functor of) the usual universal enveloping algebra. (more…)