Brace Bar-Cobar Duality
Algebraic Topology
2013-09-13 v2
Abstract
Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) \Omega : HopfAlg -> E_2 Alg, which, unlike its classical counterpart, is not strictly adjoint, but homotopically equivalent to the left adjoint of the enhanced bar construction B: E_2 Alg -> HopfAlg studied by Gerstenhaber--Voronov and Fresse.
Keywords
Cite
@article{arxiv.1309.2820,
title = {Brace Bar-Cobar Duality},
author = {Justin Young},
journal= {arXiv preprint arXiv:1309.2820},
year = {2013}
}
Comments
21 pages, added contact information