Bulletin of the Belgian Mathematical Society - Simon Stevin

Associahedron, Cyclohedron and Permutohedron as compactifications of configuration spaces

Pascal Lambrechts, Victor Turchin, and Ismar Volić

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Abstract

As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows the permutohedron with a projection to the cyclohedron, and the cyclohedron with a projection to the associahedron. We show that the preimages of any point via these projections might not be homeomorphic to (a cell decomposition of) a disk, but are still contractible. We briefly explain an application of this result to the study of knot spaces from the point of view of the Goodwillie-Weiss manifold calculus.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 2 (2010), 303-332.

Dates
First available in Project Euclid: 26 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1274896208

Digital Object Identifier
doi:10.36045/bbms/1274896208

Mathematical Reviews number (MathSciNet)
MR2663475

Zentralblatt MATH identifier
1226.51004

Subjects
Primary: 51M20: Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]
Secondary: 57N25: Shapes [See also 54C56, 55P55, 55Q07] 18D50: Operads [See also 55P48]

Keywords
polytopes cyclohedron associahedron homotopy limit

Citation

Lambrechts, Pascal; Turchin, Victor; Volić, Ismar. Associahedron, Cyclohedron and Permutohedron as compactifications of configuration spaces. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 2, 303--332. doi:10.36045/bbms/1274896208. https://projecteuclid.org/euclid.bbms/1274896208


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