Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
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
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