A Diagonal on the Associahedra

Abstract

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

References in corpus (3)

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• Closed String Field Theory: Quantum Action and the BV Master Equation
• On operad structures of moduli spaces and string theory

Cited by in corpus (6)

• The topology of spaces of knots
• Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
• Fukaya Categories as Categorical Morse Homology
• Tensor product of filtered $A_{\infty }$-algebras
• A resolution (minimal model) of the PROP for bialgebras
• Manifold theoretic compactifications of configuration spaces