Swiss-cheese action on the totalization of action-operads

Ducoulombier, Julien

doi:10.2140/agt.2016.16.1683

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Swiss-cheese action on the totalization of action-operads

Julien Ducoulombier

Algebraic & Geometric Topology 16 (2016) 1683–1726

DOI: 10.2140/agt.2016.16.1683

Abstract

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

Keywords

colored operads, loop spaces, cosimplicial spaces, model categories

Mathematical Subject Classification 2010

Primary: 55P48, 55P47

References

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

Volume 16, issue 3 (2016)