Permutohedra, configuration spaces and spineless cacti

Author

Yongheng Zhang, Purdue University

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 P_n 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.

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Committee Chair

Ralph M. Kaufmann

Date of Award

Spring 2015

Recommended Citation

Zhang, Yongheng, "Permutohedra, configuration spaces and spineless cacti" (2015). Open Access Dissertations. 607.
https://docs.lib.purdue.edu/open_access_dissertations/607

First Advisor

Ralph M. Kaufmann

Committee Member 1

James McClure

Committee Member 2

David B. McReynolds

Committee Member 3

David Gepner