Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces

Details Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces

2006-12-20

arxiv.org/abs/math/0612591v2

Mathematics

Algebraic Topology

27 pages The new version gives a more detailed exposition for the projection from the cyclohedron to the associahedron as maps

Scientific paper

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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