#### Volume 16, issue 3 (2016)

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Swiss-cheese action on the totalization of action-operads

### Julien Ducoulombier

Algebraic & Geometric Topology 16 (2016) 1683–1726
##### Abstract

We prove that, if a pair of semicosimplicial spaces $\left({X}_{c}^{\bullet };{X}_{o}^{\bullet }\right)$ arises from a colored operad, then the semitotalization has the homotopy type of a relative double loop space and the pair is weakly equivalent to an explicit algebra over the two dimensional Swiss-cheese operad ${\mathsc{S}\mathsc{C}}_{2}$.

##### Keywords
colored operads, loop spaces, cosimplicial spaces, model categories
##### Mathematical Subject Classification 2010
Primary: 55P48, 55P47
##### Publication
Received: 30 November 2014
Revised: 6 July 2015
Accepted: 13 August 2015
Published: 1 July 2016
##### Authors
 Julien Ducoulombier LAGA, CNRS, UMR 7539 Université Paris 13 99 avenue Jean-Batiste Clément 93430 Villetaneuse France