Morphisms of A-infinity Bialgebras and Applications
Abstract
We define the notion of a relative matrad and realize the free relative matrad as a free H_\infty-bimodule structure on cellular chains of bimultiplihedra JJ={JJ_{n,m} = JJ_{m,n}}. We define a morphism G:A => B of A_\infty-bialgebras as a bimodule over H_\infty and prove that the homology of every A_\infty-bialgebra over a commutative ring with unity admits an induced A_\infty-bialgebra structure. We extend the Bott-Samelson isomorphism to an isomorphism of A_\infty-bialgebras and identify the A_\infty-bialgebra structure of H_*(\Omega\Sigma X; Q). For each n>1, we construct a space X_n and identify an induced nontrivial A_\infty-bialgebra operation \omega_2^n : H^*(\Omega X_n; Z_2)^2 -> H^*(\Omega X_n; Z_2)^n.
Cite
@article{arxiv.1106.5090,
title = {Morphisms of A-infinity Bialgebras and Applications},
author = {Samson Saneblidze and Ronald Umble},
journal= {arXiv preprint arXiv:1106.5090},
year = {2012}
}
Comments
37 pages; 6 figures. The introduction in version 5 revises the introduction in version 4