The Michigan Mathematical Journal

A proof of the gap labeling conjecture

Jerome Kaminker and Ian Putnam

Full-text: Open access

Article information

Michigan Math. J., Volume 51, Issue 3 (2003), .

First available in Project Euclid: 8 December 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L87: Noncommutative differential geometry [See also 58B32, 58B34, 58J22] 52C23: Quasicrystals, aperiodic tilings
Secondary: 19K14: $K_0$ as an ordered group, traces 82D25: Crystals {For crystallographic group theory, see 20H15}


Kaminker, Jerome; Putnam, Ian. A proof of the gap labeling conjecture. Michigan Math. J. 51 (2003), no. 3, . doi:10.1307/mmj/1070919558.

Export citation


  • J. Bellissard, Gap labelling theorems for Schrödinger operators, From number theory to physics (M. Waldschmidt, P. Moussa, J. M. Luck, C. Itzykson, eds.), Springer Proc. Physics, 47, pp. 140--150, Springer-Verlag, Berlin, 1990.
  • J. Bellissard, R. Benedetti, and J.-M. Gambaudo, Spaces of tilings, finite telescopic approximation and gap labelings, preprint, 2001.
  • J. Bellissard, D. J. L. Herrmann, and M. Zarrouati, Hulls of aperiodic solids and gap labeling theorems, Directions in mathematical quasicrystals (M. Baake, R. V. Moody, eds.), pp. 207--258, Amer. Math. Soc., Providence, RI, 2000.
  • M. Benameur and H. Oyono-Oyono, Calcul du label des gaps pour les quasi-cristaux, C. R. Acad. Sci. Paris Sér. I Math. 334 (2002), 667--670.
  • L. G. Brown, P. Green, and M. A. Rieffel, Stable isomorphism and strong Morita equivalence of $C^*$-algebras, Pacific J. Math. 71 (1977), 349--363.
  • A. Connes, Sur la théorie non commutative de l'intégration, Algebres d'operateurs (Les Plans-sur-Bex, 1978), pp. 19--143, Springer-Verlag, Berlin, 1979.
  • ------, Noncommutative geometry, Academic Press, San Diego, 1994.
  • A. N. Dranishnikov, Cohomological dimension theory of compact metric spaces, preprint, 2000.
  • T. Fack and G. Skandalis, Connes' analogue of the Thom isomorphism for the Kasparov groups, Invent. Math. 64 (1981), 7--14.
  • J. Kellendonk and I. F. Putnam, Tilings, $C^*$-algebras and K-theory, Directions in mathematical quasicrystals (M. Baake, R. V. Moody, eds.), pp. 177--206, Amer. Math. Soc., Providence, RI, 2000.
  • C. C. Moore and C. Schochet, Global analysis on foliated spaces, Math. Sci. Res. Inst. Publ., 9, Springer-Verlag, New York, 1988.
  • A. L. T. Paterson, Groupoids, inverse semigroups, and their operator algebras, Birkhäuser, Boston, 1999.
  • G. Pedersen, $C^*$-algebras and their automorphism groups, Academic Press, New York, 1979.
  • M. A. Rieffel, Applications of strong Morita equivalence to transformation group $C^*$-algebras, Operator algebras and applications, part 1 (Richard V. Kadison, ed.), pp. 299--310, Amer. Math. Soc., Providence, RI, 1982.
  • L. Sadun and R. F. Williams, Tiling spaces are Cantor set fiber bundles, Ergodic Theory Dynam. Systems 23 (2003), 307--316.