Associahedron, cyclohedron and permutohedron as compactifications of configuration spaces. (English) Zbl 1226.51004

It is well-known that associahedra and cyclohedra can be defined as compactifications of configuration spaces. The authors show how 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. The authors show that the preimages of any point via these projections might not be homeomorphic to a disk, but are still contractible. They also briefly explain an application of this result to the study of knot spaces from the point of view of the Goodwillie-Weiss manifold calculus.


51M20 Polyhedra and polytopes; regular figures, division of spaces
57N25 Shapes (aspects of topological manifolds)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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