Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces
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.
Keywords
Cite
@article{arxiv.math/0612591,
title = {Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces},
author = {P. Lambrechts and V. Tourtchine and I. Volic},
journal= {arXiv preprint arXiv:math/0612591},
year = {2009}
}
Comments
27 pages The new version gives a more detailed exposition for the projection from the cyclohedron to the associahedron as maps of compactifications of configuration spaces. We also develop a similar picture for the projection from the permutohedron to the cyclohedron/associahedron