## Algebraic & Geometric Topology

### The relative lattice path operad

Alexandre Quesney

#### Abstract

We construct a set-theoretic coloured operad $ℛ ℒ$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 3 (2018), 1753-1798.

Dates
Revised: 18 November 2017
Accepted: 17 December 2017
First available in Project Euclid: 26 April 2018

https://projecteuclid.org/euclid.agt/1524708105

Digital Object Identifier
doi:10.2140/agt.2018.18.1753

Mathematical Reviews number (MathSciNet)
MR3784018

Zentralblatt MATH identifier
06866412

#### Citation

Quesney, Alexandre. The relative lattice path operad. Algebr. Geom. Topol. 18 (2018), no. 3, 1753--1798. doi:10.2140/agt.2018.18.1753. https://projecteuclid.org/euclid.agt/1524708105

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