Fetching the paper…
Reading the bibliography…
We prove that noncommutative solenoids are limits, in the sense of the Gromov-Hausdorff propinquity, of quantum tori.
F. Hausdorff, Grundzüge der Mengenlehre , Verlag Von Veit und Comp., 1914
1914
Earlier work this paper cites.
O. Bratteli and D. Robinson, Operator algebras and quantum statistical mechanics i , Springer-Verlag, 1979
1979
Earlier work this paper cites.
M. Gromov, Groups of polynomial growth and expanding maps , Publications mathématiques de l’ I. H. E. S. 53
1981
Earlier work this paper cites.
A. Connes, Compact metric spaces, Fredholm modules and hyperfiniteness , Ergodic Theory and Dynamical Systems 9
1989
Earlier work this paper cites.
J. Madore, The commutative limit of a matrix geometry , Journal of Math. Phys. 32
1991
Earlier work this paper cites.
A. Connes, M. Douglas, and A. Schwarz, Noncommutative geometry and matrix theory: Compactification on tori , JHEP 9802
1998
Earlier work this paper cites.
M. A. Rieffel, Metrics on states from actions of compact groups , Documenta Mathematica 3
1998
Earlier work this paper cites.
by same author, Metric structures for Riemannian and non-Riemannian spaces , Progress in Mathematics, Birkhäuser, 1999
1999
Earlier work this paper cites.
J. Madore, An introduction to noncommutative differential geometry and its physical applications , 2nd ed., London Mathematical Society Lecture Notes, vol. 257, Cambridge University Press, 1999
1999
Earlier work this paper cites.
by same author, Metrics on state spaces , Documenta Math. 4
1999
Earlier work this paper cites.
N. Weaver, Lipschitz algebras , World Scientific, 1999
1999
Cited alongside, same era.
M. Douglas and N. Nebrakov, Noncommutative field theory , Review of Modern Physics 73
2001
Cited alongside, same era.
W. Taylor, M(atrix) theory: matrix quantum mechanics as a fundamental theory , Review of Modern Physics 73
2001
Cited alongside, same era.
by same author, Gromov-Hausdorff distance for quantum metric spaces , Mem. Amer. Math. Soc. 168
2004
Cited alongside, same era.
F. Latrémolière, Approximation of the quantum tori by finite quantum tori for the quantum Gromov-Hausdorff distance , Journal of Funct. Anal. 223
2005
Cited alongside, same era.
by same author, Leibniz seminorms for "matrix algebras converge to the sphere" , Clay Math. Proc. 11
by same author, The triangle inequality and the dual Gromov-Hausdorff propinquity , Accepted in Indiana University Journal of Mathematics (2014), 16 Pages., ArXiv: 1404.6633
2014
Later among the works it cites.
by same author, Explicit constructions of equivalence bimodules between noncommutative solenoids , Cont. Math. (2014), 30 pages
2014
Later among the works it cites.
K. Aguilar and F. Latrémolière, Quantum ultrametrics on af algebras and the Gromov–Hausdorff propinquity , Studia Mathematica 231
2015
Later among the works it cites.
by same author, Curved noncommutative tori as Leibniz compact quantum metric spaces , Journal of Math. Phys. 56
2015
Later among the works it cites.
by same author, The dual Gromov–Hausdorff Propinquity , Journal de Mathématiques Pures et Appliquées 103
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2010
Cited alongside, same era.
F. Latrémolière and J. Packer, Noncommutative solenoids , Accepted in New York Journal of Mathematics (2011), 30 pages, ArXiv: 1110.6227
2011
Cited alongside, same era.
by same author, Noncommutative solenoids and their projective modules , Contemp. Math. 603
2013
Cited alongside, same era.
by same author, Convergence of fuzzy tori and quantum tori for the quantum Gromov–Hausdorff Propinquity: an explicit approach. , Accepted, Münster Journal of Mathematics (2014), 41 pages, ArXiv: math/1312.0069
2014
Cited alongside, same era.
by same author, Quantum metric spaces and the Gromov-Hausdorff propinquity , Accepted in Contemp. Math. (2015), 88 pages, ArXiv: 150604341
2015
Later among the works it cites.
by same author, The Quantum Gromov-Hausdorff Propinquity , Trans. Amer. Math. Soc. 368
2015
Later among the works it cites.
by same author, Matricial bridges for "matrix algebras converge to the sphere" , Submitted (2015), 31 pages, ArXiv: 1502.00329
2015
Later among the works it cites.
by same author, A compactness theorem for the dual Gromov-Hausdorff propinquity , Accepted in Indiana University Journal of Mathematics (2016), 40 Pages, ArXiv: 1501.06121
2016
Closest in time.