Diagonals on the Permutahedra, Multiplihedra and Associahedra
Abstract
We construct an explicit diagonal \Delta_P on the permutahedra P. Related diagonals on the multiplihedra J and the associahedra K are induced by Tonks' projection P > K and its factorization through J. We introduce the notion of a permutahedral set Z and lift \Delta_P to a diagonal on Z. We show that the double cobar construction \Omega^2(C_*(X)) is a permutahedral set; consequently \Delta_P lifts to a diagonal on \Omega^2(C_*(X)). Finally, we apply the diagonal on K to define the tensor product of A_\infty(co)algebras in maximal generality.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2002
 DOI:
 10.48550/arXiv.math/0209109
 arXiv:
 arXiv:math/0209109
 Bibcode:
 2002math......9109S
 Keywords:

 Mathematics  Algebraic Topology;
 55P35;
 55U05
 EPrint:
 45 pages, 13 figures. This (final) version is significantly more detailed than the previous