Matrads, Biassociahedra and A_{\infty}-Bialgebras

Details Matrads, Biassociahedra and A_{\infty}-Bialgebras Matrads, Biassociahedra and A_{\infty}-Bialgebras

2005-07-31

arxiv.org/abs/math/0508017v9

Mathematics

Algebraic Topology

54 pages; 22 Figures. Version 9 reorganizes the content of version 7 (v.8 posted incorrectly) and includes proofs of the follo

Scientific paper

We introduce the notion of a matrad M = {M_{n,m}} whose submodules M_{*,1} and M_{1,*} are non-Sigma operads. We define the free matrad H_{\infty} generated by a singleton in each bidegree (m,n) and realize H_{\infty} as the cellular chains on biassociahedra KK_{n,m} = KK_{m,n}, of which KK_{n,1} = KK_{1,n} is the associahedron K_{n}. We construct the universal enveloping functor from matrads to PROPs and define an A_{\infty}-bialgebra as an algebra over H_{\infty}.

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