Algebraic & Geometric Topology

The relative lattice path operad

Alexandre Quesney

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Abstract

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

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

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

Permanent link to this document
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

Subjects
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]

Keywords
relative lattice path operad Swiss cheese operad

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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