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.
Citation
Pascal Lambrechts. Victor Turchin. Ismar Volić. "Associahedron, Cyclohedron and Permutohedron as compactifications of configuration spaces." Bull. Belg. Math. Soc. Simon Stevin 17 (2) 303 - 332, april 2010. https://doi.org/10.36045/bbms/1274896208
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