#### Volume 18, issue 3 (2018)

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Other MSP Journals
The relative lattice path operad

### Alexandre Quesney

Algebraic & Geometric Topology 18 (2018) 1753–1798
##### Abstract

We construct a set-theoretic coloured operad $\mathsc{ℛ}\mathsc{ℒ}$ that may be thought of as a combinatorial model for the Swiss cheese operad. This is the relative (or Swiss cheese) version of the lattice path operad constructed by Batanin and Berger. By adapting their condensation process we obtain a topological (resp.  chain) operad that we show to be weakly equivalent to the topological (resp.  chain) Swiss cheese operad.

##### Keywords
relative lattice path operad, Swiss cheese operad
##### Mathematical Subject Classification 2010
Primary: 18D50
Secondary: 18G30, 55P48
##### Publication
Received: 18 July 2017
Revised: 18 November 2017
Accepted: 17 December 2017
Published: 3 April 2018
##### Authors
 Alexandre Quesney Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo São Carlos Brazil