Abstract
dc:description.abstract<p>It has been known that the configuration space F(R<sup>2</sup>, <em>n)</em> of <em>n</em> distinct ordered points in R<sup>2</sup> deformation retracts to a regular CW complex with <em>n!</em>permutohedra <em>P<sub>n</sub></em> as the top dimensional cells. In this paper, we show that there exists a similar but different permutohedral structure of the space<em>Cact(n)</em> of spineless cacti with n lobes. Based on these structures, direct homotopy equivalences between <em>F</em> (R<sup>2</sup>, <em>n)</em> and <em>Cact(n)</em> are then given. It is well known that the little 2-discs space <em>D<sub>2</sub>(n)</em> is homotopy equivalent to<em>F</em>(R<sup>2</sup>, <em>n).</em> Our results give partial combinatorial and geometrical interpretation of the equivalences between <em>D<sub>2</sub></em> and <em>Cact.</em></p>
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy (PhD)
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Year
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Zhang, Yongheng
- Contributors dc:contributor
-
- Ralph M. Kaufmann
- James McClure
- David B. McReynolds
- David Gepner
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Repository record dc:identifier
- https://docs.lib.purdue.edu/open_access_dissertations/607
- OAI identifier oai:identifier
- oai:docs.lib.purdue.edu:open_access_dissertations-1602