Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces

Simple item page
dc.creatorLambrechts, P.
dc.creatorTourtchine, V.
dc.creatorVolic, I.
dc.date2006-12-20
dc.date2009-04-23
dc.date.accessioned2026-07-07T13:07:24Z
dc.date.available2026-07-07T13:07:24Z
dc.descriptionAs 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.
dc.description27 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
dc.identifierhttps://arxiv.org/abs/math/0612591
dc.identifierhttp://arxiv.org/abs/math/0612591
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228079
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject51M20 (Secondary) 57N25, 18D50 (Secondary)
dc.titleAssociahedron, cyclohedron, and permutohedron as compactifications of configuration spaces
dc.typetext

Files

Collections

arXiv