Algebraic & Geometric Topology

The relative lattice path operad

Alexandre Quesney

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We construct a set-theoretic coloured operad 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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D50: Operads [See also 55P48]
Secondary: 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 55P48: Loop space machines, operads [See also 18D50]

relative lattice path operad Swiss cheese operad


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

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