{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1050"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1050","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori","abstract":"In this document we solve some local connectivity problems in matrix representations of the form C(T^N) -> M_n and C(T^N) -> M_n <- C([-1, 1]^N) using the so called toroidal matrix links, which can be interpreted as normal contractive matrix analogies of free homotopies in algebraic topology. In order to deal with the locality constraints, we have combined some techniques introduced in this document with several versions of the Basic Homotopy Lemma L.2.3.2, T.2.3.1 and C.2.3.1 obtained initially by Bratteli, Elliot, Evans and Kishimoto in [4] and generalized by Lin in [19] and [22]. We have also implemented some techniques from matrix geometry, combinatorial optimization and noncommutative topology developed by Loring [24, 27], Shulman [27], Bhatia [2], Chu [8], Brockett [5], Choi [7, 6], Effros [6], Exel [11], Eilers [11], Elsner [12], Pryde [31, 30], McIntosh [30] and Ricker [30].","abstract_html":"In this document we solve some local connectivity problems in matrix representations of the form C(T^N) -&gt; M_n and C(T^N) -&gt; M_n &lt;- C([-1, 1]^N) using the so called toroidal matrix links, which can be interpreted as normal contractive matrix analogies of free homotopies in algebraic topology. In order to deal with the locality constraints, we have combined some techniques introduced in this document with several versions of the Basic Homotopy Lemma L.2.3.2, T.2.3.1 and C.2.3.1 obtained initially by Bratteli, Elliot, Evans and Kishimoto in [4] and generalized by Lin in [19] and [22]. We have also implemented some techniques from matrix geometry, combinatorial optimization and noncommutative topology developed by Loring [24, 27], Shulman [27], Bhatia [2], Chu [8], Brockett [5], Choi [7, 6], Effros [6], Exel [11], Eilers [11], Elsner [12], Pryde [31, 30], McIntosh [30] and Ricker [30].","abstract_has_math":false,"creators":["Vides Romero, Fredy Antonio"],"institution":null,"degree_name":"Mathematics","degree_level":"Doctoral","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Loring, Terry A.","Terry A. Loring","Alexandru Buium","Charles Boyer","Judith Packer"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-08-25T07:00:00Z","date_published":"2016-08-25T07:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["Matrix homotopy","relative lifting problems","matrix representation","noncommutative semialgebraic sets","K-theory","amenable C*-algebra","joint spectrum."],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/51"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/51","href":"https://digitalrepository.unm.edu/math_etds/51","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/33060","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Loring, Terry A.","Terry A. 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In order to deal with the locality constraints, we have combined some techniques introduced in this document with several versions of the Basic Homotopy Lemma L.2.3.2, T.2.3.1 and C.2.3.1 obtained initially by Bratteli, Elliot, Evans and Kishimoto in [4] and generalized by Lin in [19] and [22]. We have also implemented some techniques from matrix geometry, combinatorial optimization and noncommutative topology developed by Loring [24, 27], Shulman [27], Bhatia [2], Chu [8], Brockett [5], Choi [7, 6], Effros [6], Exel [11], Eilers [11], Elsner [12], Pryde [31, 30], McIntosh [30] and Ricker [30]."]},{"key":"dc:title","label":"Title","values":["Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori"]}]}],"canonical_facts":{"dc:contributor":["Loring, Terry A.","Terry A. Loring","Alexandru Buium","Charles Boyer","Judith Packer"],"dc:creator":["Vides Romero, Fredy Antonio"],"dc:description.abstract":["In this document we solve some local connectivity problems in matrix representations of the form C(T^N) -> M_n and C(T^N) -> M_n <- C([-1, 1]^N) using the so called toroidal matrix links, which can be interpreted as normal contractive matrix analogies of free homotopies in algebraic topology. In order to deal with the locality constraints, we have combined some techniques introduced in this document with several versions of the Basic Homotopy Lemma L.2.3.2, T.2.3.1 and C.2.3.1 obtained initially by Bratteli, Elliot, Evans and Kishimoto in [4] and generalized by Lin in [19] and [22]. We have also implemented some techniques from matrix geometry, combinatorial optimization and noncommutative topology developed by Loring [24, 27], Shulman [27], Bhatia [2], Chu [8], Brockett [5], Choi [7, 6], Effros [6], Exel [11], Eilers [11], Elsner [12], Pryde [31, 30], McIntosh [30] and Ricker [30]."],"dc:identifier":["http://hdl.handle.net/1928/33060","https://digitalrepository.unm.edu/math_etds/51"],"dc:language":["English"],"dc:subject":["Matrix homotopy","relative lifting problems","matrix representation","noncommutative semialgebraic sets","K-theory","amenable C*-algebra","joint spectrum."],"dc:title":["Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Doctoral","Dissertation"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}