Morphisms of A-infinity Bialgebras and Applications

الأصل · EN

We define the notion of a relative matrad and realize the free relative matrad as a free H∞-bimodule structure on cellular chains of bimultiplihedra JJ=JJₙ,ₘ = JJₘ,ₙ. We define a morphism G:A => B of A∞-bialgebras as a bimodule over H∞ and prove that the homology of every A∞-bialgebra over a commutative ring with unity admits an induced A∞-bialgebra structure. We extend the Bott-Samelson isomorphism to an isomorphism of A∞-bialgebras and identify the A∞-bialgebra structure of H*(ΩΣX; Q). For each n>1, we construct a space Xₙ and identify an induced nontrivial A∞-bialgebra operation ω₂ⁿ: H*(ΩXₙ; Z₂)² -> H*(ΩXₙ; Z₂)ⁿ.