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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 (Xc;Xo) arises from a colored operad, then the semitotalization  sTot(Xo) has the homotopy type of a relative double loop space and the pair ( sTot(Xc); sTot(Xo)) is weakly equivalent to an explicit algebra over the two dimensional Swiss-cheese operad SC2.

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