Open Access
January 2018 Local matrix homotopies and soft tori
Terry A. Loring, Fredy Vides
Banach J. Math. Anal. 12(1): 167-190 (January 2018). DOI: 10.1215/17358787-2017-0048


We present solutions to local connectivity problems in matrix representations of the form C([1,1]N)C(uε,vε), with Cε(T2)C(uε,vε) for any ε[0,2] and any integer n1, where C(uε,vε)Mn is an arbitrary matrix representation of the universal C-algebra Cε(T2) that denotes the soft torus. We solve the connectivity problems by introducing the so-called toroidal matrix links, which can be interpreted as normal contractive matrix analogies of free homotopies in differential algebraic topology.

To deal with the locality constraints, we have combined some techniques introduced in this article with some techniques from matrix geometry, combinatorial optimization, and classification and representation theory of C-algebras.


Download Citation

Terry A. Loring. Fredy Vides. "Local matrix homotopies and soft tori." Banach J. Math. Anal. 12 (1) 167 - 190, January 2018.


Received: 29 November 2016; Accepted: 22 March 2017; Published: January 2018
First available in Project Euclid: 17 November 2017

zbMATH: 06841270
MathSciNet: MR3745579
Digital Object Identifier: 10.1215/17358787-2017-0048

Primary: 46L85
Secondary: 20F65 , 22D25 , 65J22

Keywords: amenable C∗-algebra , joint spectrum , matrix homotopy , matrix representation , relative lifting problems

Rights: Copyright © 2018 Tusi Mathematical Research Group

Vol.12 • No. 1 • January 2018
Back to Top