Date of Award
Spring 2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Ralph M. Kaufmann
Committee Chair
Ralph M. Kaufmann
Committee Member 1
James McClure
Committee Member 2
David B. McReynolds
Committee Member 3
David Gepner
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 spaceCact(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 toF(R2, n). Our results give partial combinatorial and geometrical interpretation of the equivalences between D2 and Cact.
Recommended Citation
Zhang, Yongheng, "Permutohedra, configuration spaces and spineless cacti" (2015). Open Access Dissertations. 607.
https://docs.lib.purdue.edu/open_access_dissertations/607