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University of Illinois at Urbana-Champaign
On State Complexes and Special Cube Complexes
Abstract
dc:descriptionWe find that state complexes are non-positively curved metric spaces, aspherical topological spaces, and have fundamental groups that are subgroups of right-angled Artin groups. In addition, we find that the property state is preserved when taking finite products, as is true in the case of special. Unlike special, however, state is not inherited by convex subcomplexes or finite covers; the latter fact is somewhat surprising to experts. Several other classification results are presented, along with methods for realization; we conclude with directions for further study. Numerous examples and figures supplement the text.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Peterson, Valerie J.
- Contributors dc:contributor
-
- Robert W. Ghrist
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3395575
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86935