Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori

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].

Name thesis:degree_name

Mathematics

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics & Statistics

Year

2016

Author dc:creator

• Vides Romero, Fredy Antonio

Contributors dc:contributor

• Loring, Terry A.
• Terry A. Loring
• Alexandru Buium
• Charles Boyer
• Judith Packer

• Matrix homotopy
• relative lifting problems
• matrix representation
• noncommutative semialgebraic sets
• K-theory
• amenable C*-algebra
• joint spectrum.

Language dc:language

English

Identifier

https://digitalrepository.unm.edu/math_etds/51

OAI identifier oai:identifier

oai:digitalrepository.unm.edu:math_etds-1050