Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

The symmetric join operad

Pages: 245 – 265

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a15


Michał Adamaszek (Mathematics Institute, Universität Bremen, Germany)

John D. S. Jones (Mathematics Institute, University of Warwick, Coventry, United Kingdom)


The join operad arises from the combinatorial study of the iterated join of simplices. We study a suitable simplicial version of this operad that includes the symmetries given by permutations of the factors of the join. This is the symmetric join operad. As an application of this combinatorics we construct an $E_{\infty}$-operad that coacts naturally on the chains of a simplicial set.


join, operads, $E_{\infty}$, cochain operations

2010 Mathematics Subject Classification

18D50, 55U10, 55U15

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Published 4 December 2014