Banach Journal of Mathematical Analysis

Local matrix homotopies and soft tori

Terry A. Loring and Fredy Vides

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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.

Article information

Banach J. Math. Anal., Volume 12, Number 1 (2018), 167-190.

Received: 29 November 2016
Accepted: 22 March 2017
First available in Project Euclid: 17 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L85: Noncommutative topology [See also 58B32, 58B34, 58J22]
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 65J22: Inverse problems

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


Loring, Terry A.; Vides, Fredy. Local matrix homotopies and soft tori. Banach J. Math. Anal. 12 (2018), no. 1, 167--190. doi:10.1215/17358787-2017-0048.

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