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The relative lattice path operad

Alexandre Quesney

Algebraic & Geometric Topology 18 (2018) 1753–1798

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.

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