Publication Date
8-25-2016
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].
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Terry A. Loring
Second Committee Member
Alexandru Buium
Third Committee Member
Charles Boyer
Fourth Committee Member
Judith Packer
Language
English
Keywords
Matrix homotopy, relative lifting problems, matrix representation, noncommutative semialgebraic sets, K-theory, amenable C*-algebra, joint spectrum.
Document Type
Dissertation
Recommended Citation
Vides Romero, Fredy Antonio. "Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori." (2016). https://digitalrepository.unm.edu/math_etds/51
