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…)

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Universal enveloping e_n-algebra

Posted in Mathematics by nikitamarkarian on July 30, 2011

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…)