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Title:On State Complexes and Special Cube Complexes
Author(s):Peterson, Valerie J.
Doctoral Committee Chair(s):Robert W. Ghrist
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:We 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.
Issue Date:2009
Type:Text
Language:English
Description:98 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.
URI:http://hdl.handle.net/2142/86935
Other Identifier(s):(MiAaPQ)AAI3395575
Date Available in IDEALS:2015-09-28
Date Deposited:2009


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