Date of Award

Spring 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)



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


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.

Included in

Mathematics Commons