{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101517"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101517","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Intertwined symmetry and topology in 3 + 1 dimensional gapped quantum phases of matter","abstract":"This thesis is an investigation of various topological properties of 3 + 1 dimensional Bosonic gapped phases of matter. We divide our study into two main themes, the first involving short-range entangled phases with global symmetries also known as symmetry protected topological phases and the second involving phases with long range entanglement also known as topologically ordered phases.","abstract_html":"This thesis is an investigation of various topological properties of 3 + 1 dimensional Bosonic gapped phases of matter. 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