Associahedron, Cyclohedron and Permutohedron as compactifications of configuration spaces

作者：Lambrechts Pascal^*; Turchin Victor; Volic Ismar

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2010, 17(2): 303-332.

• polytopes
• cyclohedron
• associahedron
• homotopy limit

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.

• 出版日期2010-6