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- W3208343277 abstract "We complete the construction of the biassociahedra $KK$, construct the free matrad $mathcal{H}_{infty}$, realize $mathcal{H}_{infty}$ as the cellular chains of $KK,$ and define an $A_{infty}$-bialgebra as an algebra over $mathcal{H}_{infty}.$ We construct the bimultiplihedra $JJ,$ construct the relative free matrad $rmathcal{H}_{infty}$ as a $mathcal{H}_{infty}$-bimodule, realize $rmathcal{H}_{infty}$ as the cellular chains of $JJ$, and define a morphism of $A_{infty}$-bialgebras as a bimodule over $mathcal{H}_{infty}$. We 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 determine the $A_{infty} $-bialgebra structure of $H_{ast}left( OmegaSigma X;mathbb{Q}right) $. For each $ngeq2$, we construct a space $X_{n}$ and identify an induced nontrivial $A_{infty}$-bialgebra operation $omega_{2}^{n}: H^{ast}left(Omega X_{n};mathbb{Z}_{2}right) ^{otimes2}rightarrow H^{ast}left(Omega X_{n};mathbb{Z}_{2}right) ^{otimes n}$." @default.
- W3208343277 created "2021-11-08" @default.
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- W3208343277 date "2021-10-22" @default.
- W3208343277 modified "2023-09-27" @default.
- W3208343277 title "Framed Matrices and $A_{infty}$-Bialgebras" @default.
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