Comparing diagonals on the associahedra. (English) Zbl 07860682
Summary: We prove that the formula for the diagonal approximation \(\Delta_K\) on J. Stasheff’s \(n\)-dimensional associahedron \(K_{n+2}\) derived by the current authors in [7] agrees with the “magical formula” for the diagonal approximation \(\Delta^\prime_K\) derived by Markl and Shnider in [5], by J.-L. Loday in [4], and more recently by Masuda, Thomas, Tonks, and Vallette in [6].
MSC:
| 55P48 | Loop space machines and operads in algebraic topology |
| 55P99 | Homotopy theory |
| 52B05 | Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) |
| 52B11 | \(n\)-dimensional polytopes |
