Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces

2006/12/20 by Lambrechts, P., Tourtchine, V., Volic, I. · 1 citation
#18D50 (Secondary) #51M20 (Secondary) 57N25 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0612591

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.

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Related

• P-associahedra
• Graphical configuration spaces, Contractads and Formality
• Manifold theoretic compactifications of configuration spaces
• A space of cyclohedra
• Configuration spaces of points on the circle and hyperbolic Dehn fillings