Twisted index theory on good orbifolds, I: Noncommutative Bloch theory

Communications in Contemporary Mathematics

Volumn 1, Issue 4, 1999, Pages 553-587

  Marcolli, Matilde ^a   Mathai, Varghese ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844456180     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199799000213     Document Type: Article

References (41)

1. M. F. Atiyah, Elliptic operators, discrete groups and Von Neumann algebras, Astérisque 32-33 (1976) 43-72.
2. M. F. Atiyah, R. Bott and V. K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973) 279-330.
3. M. F. Atiyah and I. M. Singer, The index of elliptic operators III, Ann. of Math. 87 (1968) 546-604.
4. P. Baum and A. Connes, Chern Character for discrete groups, A fete of Topology, Academic Press (1988) 163-232.
5. P. Baum, A. Connes and N. Higson, Classifying space for proper actions and K-theory of group C*-algebras, Contemp. Math. 167 (1994) 241-291.
6. J. Bellissard, A. van Elst and H. Schulz-Baldes, The non-commutative geometry of the quantum Hall effect, J. Math. Phys. 35 (1994) 5373-5451.
7. A. Broughton, Classifying finite group actions on surfaces of low genus, J. Pure Appl. Algebra 69 (1991) 233-270.
8. J. Brüning and T. Sunada, On the spectrum of gauge-periodic elliptic operators, Méthodes semi-classiques, Vol. 2 (Nantes, 1991).
9. Astérisque 210 (1992) 65-74.
10. A. Carey, K. Hannabuss, V. Mathai and P. McCann, Quantum Hall Effect on the hyperbolic plane, Commun. Math. Physics 190 (1997) 629-673.
11. J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds, Jour. Diff. Geom. 17 (1982) 15-54.
12. A. Connes, Noncommutative differential geometry, Publ. Math. I.H.E.S. 62 (1986) 257-360.
13. A. Connes, Noncommutative geometry, Academic Press, Inc., San Diego, CA (1994).
14. J. Cuntz, K-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 (1983) 180-195.
15. G. Elliott, On the K-theory of the C*-algebra generated by a projective representation of a torsion-free discrete group, Operator Algebras and Group Representations, Pitman, London (1983) 157-184.
16. C. Farsi, K-theoretical index theorems for good orbifolds, Proc. Amer. Math. Soc. 115 (1992) 769-773.
17. M. Furuta and B. Steer, Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points, Adv. Math. 96 (1992) 38-102.
18. E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986) 111-117.
19. P. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, Math. Lect. Series Vol. 11, Publish or Perish Inc., 1984.
20. P. Green, The structure of imprimitivity algebras, J. Func. Anal. 36 (1980) 88-104.
21. 2 Hodge theory, J. Diff. Geom. 33 (1991) 263-292.
22. P. Julg, K-théorie équivariante et produits croisés., C. R. Acad. Sci. Paris, Sér. I Math. 292 (1981) 629-632.
23. P. Julg and G. Kasparov, Operator K-theory for the group SU(n, 1), J. Reine Angew. Math. 463 (1995) 99-152.
24. G. Kasparov, Lorentz groups, K-theory of unitary representations and crossed products, Soviet Math. Dokl. 29 (1984) 256-260.
25. G. Kasparov, K-theory, group C*-algebras and higher signatures, Conspectus, (1980), published in 'Novikov conjectures, index theorems and rigidity', Vol. 1,
26. eds. S. Ferry, A. Ranicki and J. Rosenberg, Lond. Math. Soc. Lecture Note Series 226 (1995), Cambridge University Press.
27. T. Kawasaki, The index of elliptic operators over V-manifolds, Nagoya Math. Jour. 84 (1981) 135-157.
28. Y. Last, Almost everything about the almost Mathieu operator. I, XIth International Congress of Mathematical Physics (Paris, 1994) 366-372, Internat. Press, Cambridge, MA, 1995.
29. M. Marcolli and V. Mathai, Twisted higher index theory on good orbifolds and fractional quantum numbers, math.DG/9803051.
30. V. Mathai, K-theory of twisted group C*-algebras and positive scalar curvature, Rothenberg Festschrift, Contemporary Mathematics 231 (1999) 203-225.
31. J. McCleary, User's guide to spectral sequences. Mathematics Lecture Series, Vol. 12. Publish or Perish, Inc., Wilmington, Del., 1985.
32. A. Mishchenko and A. Fomenko, The index of elliptic operators over C* algebras, Math. UUSR Izv. 15 (1980) 87-112.
33. J. Packer and I. Raeburn, Twisted cross products of C*-algebras, Math. Proc. Camb. Phil. Soc. 106 (1989) 293-311.
34. J. Packer and I. Raeburn, Twisted cross products of C*-algebras. II, Math. Ann. 287 (1990) 595-612.
35. J. Roe, Elliptic operators, topology and asymptotic methods, Pitman research notes in mathematics 179, Longman, 1988.
36. J. Rosenberg, C*-algebras, positive scalar curvature, and the Novikov conjecture-III, Topology 25 (1986) 319-336.
37. P. Sarnak, Entropy estimates for geodesic flows, Ergodic theory Dynam. Sys. 2 (1982) 513-524.
38. I. Satake, The Gauss-Bonnet theorem for V-manifolds, J. Math. Soc. Japan 9 (1957) 464-492.
39. P. Scott, The geometries of S-manifolds, Bull. Lond. Math. Soc. 15 (1983) 401-487.
40. M. Shubin, Discrete Magnetic Schrödinger operators, Commun. Math. Phys. 164 (1994) 259-275.
41. M. M. Skriganov, Proof of the Bethe-Sommerfeld conjecture in dimension 2. Dokl. Akad. Nauk SSSR 248 (1979) 39-42.