English

The diagonal of the associahedra

Algebraic Topology 2019-02-22 v1 Combinatorics

Abstract

This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also known as Stasheff polytopes. We show that it satisfies an easy-to-state cellular formula. For the first time, we endow a family of realizations of the associahedra (the Loday realizations) with a topological and cellular operad structure; it is shown to be compatible with the diagonal maps.

Keywords

Cite

@article{arxiv.1902.08059,
  title  = {The diagonal of the associahedra},
  author = {Naruki Masuda and Hugh Thomas and Andy Tonks and Bruno Vallette},
  journal= {arXiv preprint arXiv:1902.08059},
  year   = {2019}
}

Comments

19 pages, 7 figures. Comments are welcome