{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/70379"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/70379","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants","abstract":"We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration.","abstract_html":"We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration.","abstract_has_math":false,"creators":["Otto, Carolyn Ann"],"institution":"Rice University","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Natural Sciences","degree_department":null,"school":null,"contributors":[],"advisors":["Harvey, Shelly"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-24T04:10:17Z","subjects":["Pure sciences","Knot theory","Link concordance","Solvable filtration","String links","Mathematics"],"languages":["eng"],"rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1911/70379","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Harvey, Shelly"]},{"key":"dc:creator","label":"Author","values":["Otto, Carolyn Ann"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-03-08T00:37:23Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-03-08T00:37:23Z"]},{"key":"dc:date.issued","label":"Date","values":["2011"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Natural Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Rice University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Pure sciences","Knot theory","Link concordance","Solvable filtration","String links","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1911/70379"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants"]}]}],"canonical_facts":{"dc:contributor.advisor":["Harvey, Shelly"],"dc:creator":["Otto, Carolyn Ann"],"dc:date.accessioned":["2013-03-08T00:37:23Z"],"dc:date.available":["2013-03-08T00:37:23Z"],"dc:date.issued":["2011"],"dc:description.abstract":["We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1911/70379"],"dc:language.iso":["eng"],"dc:rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"dc:subject":["Pure sciences","Knot theory","Link concordance","Solvable filtration","String links","Mathematics"],"dc:title":["The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants"],"dc:type":["Thesis"],"thesis:degree_discipline":["Natural Sciences"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Rice University"]},"updated_at":"2026-07-24T04:10:17Z"}