Fetching the paper…
Reading the bibliography…
Given a constant magnetic field on Euclidean space ${\mathbb R}^p$ determined by a skew-symmetric $(p\times p)$ matrix $\Theta$, and a ${\mathbb Z}^p$-invariant probability measure $\mu$ on the disorder set $\Sigma$ which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density of States of any self-adjoint operator affiliated to the twisted crossed product algebra $C(\Sigma) \rtimes_\sigma {\mathbb Z}^p$, where $\sigma$ is the multiplier on ${\mathbb Z}^p$ associated to $\Theta$, takes on values on spectral gaps in the magnetic gap-labelling group.
P. Green, The local structure of twisted covariance algebras. Acta Math. 140 (1978), no. 3-4, 191–250. MR0493349
1978
Earlier work this paper cites.
M. Pimsner, D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras. J. Operator Theory 4 (1980), no. 1, 93–118. MR0587369
1980
Earlier work this paper cites.
M. Pimsner, D. Voiculescu, Imbedding the irrational rotation C*-algebra into an AF-algebra. J. Operator Theory 4 (1980), no. 2, 20–210
1980
Earlier work this paper cites.
A. Connes, An analogue of the Thom isomorphism for crossed products of a C ∗ C^{*} -algebra by an action of ℝ {\mathbb{R}} . Adv. in Math. 39 (1981), no. 1, 31–55. MR0605351
1981
Earlier work this paper cites.
T. Fack, G. Skandalis, Connes’ analogue of the Thom isomorphism for the Kasparov groups. Invent. Math. 64 (1981), no. 1, 7–14. MR0621767
1981
Earlier work this paper cites.
J. Moser, An example of a Schrödinger equation with an almost periodic potential and nowhere dense spectrum. Comm. Math. Helv., 56
1981
Earlier work this paper cites.
M. Rieffel, C ∗ C^{*} -algebras associated with irrational rotations. Pacific J. Math. 93
1981
Earlier work this paper cites.
J. Bellissard, Schrödinger’s operators with an almost periodic potential : an overview. In: Lecture Notes in Phys., 153
1982
Earlier work this paper cites.
J. Bellissard, E. Scoppola, The density of states for almost periodic Schrödinger operators and the frequency module: a counter example. Comm. Math. Phys., 85
1982
Earlier work this paper cites.
K. Brown, Cohomology of groups. Graduate Texts in Mathematics, 87. Springer-Verlag, New York-Berlin, 1982. MR0672956
1982
Earlier work this paper cites.
A. Connes, A survey of foliations and operator algebras. In: Operator algebras and applications, Part I, pp. 521–628, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982 MR0679730
1982
Earlier work this paper cites.
M. Rieffel, Applications of strong Morita equivalence to transformation group C ∗ C^{*} -algebras. In: Operator algebras and applications, part 1 (Richard V. Kadison, ed.), pp. 299–310, Amer. Math. Soc., Providence, RI, 1982. MR0679709
1982
Earlier work this paper cites.
C. Schochet, Topological methods for C ∗ C^{*} -algebras. II. Geometric resolutions and the Künneth formula. Pacific J. Math. 98 (1982), no. 2, 443–458. MR0650021
1982
Earlier work this paper cites.
R. Johnson, J. Moser, The rotation number for almost periodic potentials. Comm. Math. Phys. 84 (1982), no. 3, 403-438. MR0667409; Erratum: Comm. Math. Phys. 90 (1983), no. 2, 317–318. MR0714441
1983
Earlier work this paper cites.
Connes, A., Skandalis, G. The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. 20 (1984), no. 6, 1139–1183
1984
Earlier work this paper cites.
G. Elliott, On the K-theory of the C*-algebra generated by a projective representation of a torsion-free discrete abelian group. In: Operator Algebras and Group Representations, Vol. I (Neptun, 1980), pp. 157–184, Monogr. Stud. Math., 17, Pitman, Boston, MA, 1984. MR0731772
1984
Earlier work this paper cites.
J. Bellissard, K-theory of C ∗ C^{*} -algebras in solid state physics. Statistical mechanics and field theory: mathematical aspects (Groningen, 1985). 99–156, Lecture Notes in Phys., 257, Springer, Berlin, 1986. MR0862832
1986
Cited alongside, same era.
V. Mathai, D. Quillen, Superconnections, Thom classes, and equivariant differential forms. Topology 25
1986
Cited alongside, same era.
J. Packer, I. Raeburn, Twisted crossed products of C*-algebras. Math. Proc. Cambridge Philos. Soc. 106 (1989), no. 2, 293–311. MR1002543
1989
Cited alongside, same era.
A. Connes, H. Moscovici, Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Topology 29 (1990), no. 3, 345–388. MR1066176
1990
Cited alongside, same era.
J. Packer and I. Raeburn, Twisted crossed products of C ∗ C^{*} -algebras. II. Math. Ann. 287
1990
Cited alongside, same era.
M. Marcolli, V. Mathai, Twisted index theory on good orbifolds. II: Fractional quantum numbers. Commun. Math. Phys. 217
2001
Later among the works it cites.
M.-T. Benameur, H. Oyono-Oyono, Calcul du label des gaps pour les quasi-cristaux. (French) [Computation of the gap-labelling for quasi-crystals] C. R. Math. Acad. Sci. Paris 334 (2002), no. 8, 667–670. MR1903367
2002
Later among the works it cites.
M-T. Benameur, H. Oyono-Oyono, Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard). In: Operator algebras and mathematical physics (Constanza, 2001), pp. 11–22, Bucharest, 2003. MR2018220
2003
Later among the works it cites.
J. Kaminker, I. Putnam, A proof of the gap labelling conjecture. Michigan Math. J. 51 (2003), no. 3, 537–546. MR2021006
2003
Later among the works it cites.
M.-T. Benameur, J. L. Heitsch, Index theory and non-commutative geometry. I. Higher families index theory, K-Theory 33 (2004), no. 2, 151–183
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
J. Bellissard, Gap labelling theorems for Schrödinger’s operators. In: From Number Theory to Physics pp. 538–630, Les Houches March 89, Springer, J.M. Luck, P. Moussa & M. Waldschmidt Eds., (1992). MR1221111
1992
Cited alongside, same era.
J. Bellissard, A. Bovier, J.-M. Ghez, Gap labelling theorems for one dimensional discrete Schrödinger operators. Rev. of Math. Phys., 4
1992
Cited alongside, same era.
P. Baum, A. Connes, N. Higson, Classifying space for proper actions and K K -theory of group C ∗ C^{*} -algebras. Contemp. Math. 167
1994
Cited alongside, same era.
J. Bellissard, A. van Elst, H. Schulz-Baldes, The noncommutative geometry of the quantum Hall effect. J. Math. Phys. 35
1994
Cited alongside, same era.
A. van Elst, Gap-labelling theorems for Schrödinger operators on the square and cubic lattice. Rev. Math. Phys., 6
1994
Cited alongside, same era.
J. Anderson, I. Putnam, Topological invariants for substitution tilings and their associated C ∗ C^{\ast} -algebras. Ergodic Theory Dynam. Systems, 18
1998
Cited alongside, same era.
J. Bellissard, E. Contensous, A. Legrand, K − K- théorie des quasicristaux, image par la trace: le cas du réseau octogonal. C.R.A.S t.327, Serie I, 1998, p.197–200. MR1646928
1998
Cited alongside, same era.
2004
Later among the works it cites.
N. Berline, E. Getzler, M. Vergne, Heat kernels and Dirac operators. Grundlehren Text Editions. Springer-Verlag, Berlin, 2004. MR1215720
2004
Later among the works it cites.
J. Kellendonk, Gap labelling and the pressure on the boundary. Comm. Math. Phys. 258
2005
Later among the works it cites.
J. Bellissard, R. Benedetti, J-M. Gambaudo, Spaces of tilings, finite telescopic approximations and gap-labelling. Comm. Math. Phys. 261 (2006), no. 1, 1–41. MR2193205
2006
Later among the works it cites.
C. Moore, C. Schochet, Global analysis on foliated spaces. Second edition. Mathematical Sciences Research Institute Publications, 9. Cambridge University Press, New York, 2006. MR0918974
2006
Later among the works it cites.
M.-T. Benameur, H. Oyono-Oyono, Index theory for quasi-crystals. I. Computation of the gap-label group. J. Funct. Anal. 252 (2007), no. 1, 137–170. MR2357353
2007
Later among the works it cites.
L. Parnovski, Bethe-Sommerfeld conjecture. Ann. Henri Poincaré 9 (2008), no. 3, 457–508. MR2419769
2008
Later among the works it cites.
L. Sadun, Topology of tiling spaces. University Lecture Series, 46. American Mathematical Society, Providence, RI, 2008. MR2446623
2008
Later among the works it cites.
M-T. Benameur, P. Piazza, Index, eta and rho invariants on foliated bundles. Astèrisque 327
2009
Later among the works it cites.
P. Miranda, G. Raikov, Discrete spectrum of quantum Hall effect Hamiltonians II: Periodic edge potentials. Asymptot. Anal. 79
2012
Later among the works it cites.
M. Kreisel, Gabor Frames for quasicrystals, K-theory, and twisted gap labelling. J. Funct. Anal. 270
2016
Closest in time.