Permutohedra, configuration spaces and spineless cacti
Abstract
It has been known that the configuration space F(R2, n) of n distinct ordered points in R2 deformation retracts to a regular CW complex with n! permutohedra Pn as the top dimensional cells. In this paper, we show that there exists a similar but different permutohedral structure of the space Cact(n) of spineless cacti with n lobes. Based on these structures, direct homotopy equivalences between F (R2, n) and Cact(n) are then given. It is well known that the little 2-discs space D2(n) is homotopy equivalent to F(R2, n). Our results give partial combinatorial and geometrical interpretation of the equivalences between D2 and Cact.
Degree
Ph.D.
Advisors
Kaufmann, Purdue University.
Subject Area
Mathematics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.