A proof of the gap labeling conjecture
Jerome Kaminker and Ian Putnam
Source: Michigan Math. J. Volume 51, Issue 3
(2003), .
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1070919558
Digital Object Identifier: doi:10.1307/mmj/1070919558
Mathematical Reviews number (MathSciNet): MR2021006
Zentralblatt MATH identifier: 02075169
References
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.
Mathematical Reviews (MathSciNet): MR1221111
J. Bellissard, R. Benedetti, and J.-M. Gambaudo, Spaces of tilings, finite telescopic approximation and gap labelings, preprint, 2001.
Mathematical Reviews (MathSciNet): MR2193205
Digital Object Identifier: doi:10.1007/s00220-005-1445-z
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.
Mathematical Reviews (MathSciNet): MR1798994
Zentralblatt MATH: 0972.52014
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.
Mathematical Reviews (MathSciNet): MR1903367
Digital Object Identifier: doi:10.1016/S1631-073X(02)02312-9
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.
Mathematical Reviews (MathSciNet): MR463928
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.
Mathematical Reviews (MathSciNet): MR548112
------, Noncommutative geometry, Academic Press, San Diego, 1994.
Mathematical Reviews (MathSciNet): MR1303779
Zentralblatt MATH: 0818.46076
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.
Mathematical Reviews (MathSciNet): MR621767
Digital Object Identifier: doi:10.1007/BF01393931
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.
Mathematical Reviews (MathSciNet): MR1798993
Zentralblatt MATH: 0972.52015
C. C. Moore and C. Schochet, Global analysis on foliated spaces, Math. Sci. Res. Inst. Publ., 9, Springer-Verlag, New York, 1988.
Mathematical Reviews (MathSciNet): MR918974
Zentralblatt MATH: 0648.58034
A. L. T. Paterson, Groupoids, inverse semigroups, and their operator algebras, Birkhäuser, Boston, 1999.
Mathematical Reviews (MathSciNet): MR1724106
Zentralblatt MATH: 0913.22001
G. Pedersen, $C^*$-algebras and their automorphism groups, Academic Press, New York, 1979.
Mathematical Reviews (MathSciNet): MR548006
Zentralblatt MATH: 0416.46043
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.
Mathematical Reviews (MathSciNet): MR679709
Zentralblatt MATH: 0526.46055
L. Sadun and R. F. Williams, Tiling spaces are Cantor set fiber bundles, Ergodic Theory Dynam. Systems 23 (2003), 307--316.
Mathematical Reviews (MathSciNet): MR1971208
Digital Object Identifier: doi:10.1017/S0143385702000949
The Michigan Mathematical Journal
