Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 1 (2018), 167-190.
Local matrix homotopies and soft tori
We present solutions to local connectivity problems in matrix representations of the form , with for any and any integer , where is an arbitrary matrix representation of the universal -algebra 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 -algebras.
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
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.bjma/1510909220