A Diagonal on the Associahedra

Mathematics – Algebraic Topology

Scientific paper

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Scientific paper

Let C_*(K) denote the cellular chains on the Stasheff associahedra. We
construct an explicit combinatorial diagonal \Delta : C_*(K) --> C_*(K) \otimes
C_*(K); consequently, we obtain an explicit diagonal on the A_\infty-operad. We
apply the diagonal \Delta to define the tensor product of A_\infty-(co)algebras
in maximal generality.

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