{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110496"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110496","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Knot complements and 3-manifolds","abstract":"The study of 3-manifold groups has reached big success in the last few decades, with the proof of geometrization theorem by Perelman, and several virtually compact special theorems by Wise, etc. In this paper, we will explore several aspects of 3-manifold groups and see what it shows for the knot complement as a compact 3-manifold. We will also apply some combinatorial methods in three-manifold topology to the study of the presentation of the knot complement.","abstract_html":"The study of 3-manifold groups has reached big success in the last few decades, with the proof of geometrization theorem by Perelman, and several virtually compact special theorems by Wise, etc. In this paper, we will explore several aspects of 3-manifold groups and see what it shows for the knot complement as a compact 3-manifold. 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We will also apply some combinatorial methods in three-manifold topology to the study of the presentation of the knot complement.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, Lecheng Su, accepted the attached license on 2021-04-17 at 20:12.","The student, Lecheng Su, submitted this Thesis for approval on 2021-04-17 at 20:18.","This Thesis was approved for publication on 2021-04-26 at 16:42.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16389 on 2021-09-16 at 16:42:27","Made available in DSpace on 2021-09-17T01:11:01Z (GMT). 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We will also apply some combinatorial methods in three-manifold topology to the study of the presentation of the knot complement.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, Lecheng Su, accepted the attached license on 2021-04-17 at 20:12.","The student, Lecheng Su, submitted this Thesis for approval on 2021-04-17 at 20:18.","This Thesis was approved for publication on 2021-04-26 at 16:42.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16389 on 2021-09-16 at 16:42:27","Made available in DSpace on 2021-09-17T01:11:01Z (GMT). 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