{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86935"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86935","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On State Complexes and Special Cube Complexes","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Peterson, Valerie J."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Robert W. 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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.","Made available in DSpace on 2015-09-28T15:20:14Z (GMT). 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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.","Made available in DSpace on 2015-09-28T15:20:14Z (GMT). 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