Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

Eta-invariants and von Neumann algebras


Authors: R. G. Douglas, S. Hurder and J. Kaminker
Journal: Bull. Amer. Math. Soc. 21 (1989), 83-87
MSC (1985): Primary 58G10, 46L80, 57R30
MathSciNet review: 979832
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l’Honneur de Henri Cartan (Orsay, 1974), Soc. Math. France, Paris, 1976, pp. 43–72. Astérisque, No. 32-33. MR 0420729
  • Michael Francis Atiyah, Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Springer-Verlag, Berlin-New York, 1974. MR 0482866
  • M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69. MR 0397797
  • M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. III, Math. Proc. Cambridge Philos. Soc. 79 (1976), no. 1, 71–99. MR 0397799
  • [AS] M. F. Atiyah and I. M. Singer, Index theory for skew-adjoint Fredholm operators, Publ. Math. Inst. Hautes Études Sci. 37 (1969), 305-326.
  • Jeff Cheeger and Mikhael Gromov, On the characteristic numbers of complete manifolds of bounded curvature and finite volume, Differential geometry and complex analysis, Springer, Berlin, 1985, pp. 115–154. MR 780040
  • L. A. Coburn and R. G. Douglas, 𝐶*-algebras of operators on a half-space. I, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 59–67. MR 0358417
  • [CDSS] L. Coburn, R. G. Douglas, R. G. Schaeffer, and I. M. Singer, C*-algebras of operators on a halfspace. II: Index theory, Publ. Math. Inst. Hautes Études Sci. 40 (1971), 69-79.
  • Alain Connes, The von Neumann algebra of a foliation, Mathematical problems in theoretical physics (Proc. Internat. Conf., Univ. Rome, Rome, 1977) Lecture Notes in Phys., vol. 80, Springer, Berlin-New York, 1978, pp. 145–151. MR 518430
  • [C 2] A. Connes, Non-commutative differential geometry, I.- The Chern character in K-homology, Publ. Math. Inst. Hautes Études Sci. 62 (1986), 257-309.
  • R. G. Douglas, Elliptic invariants for differential operators, The mathematical heritage of Hermann Weyl (Durham, NC, 1987) Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, RI, 1988, pp. 275–284. MR 974341, 10.1090/pspum/048/974341
  • Ronald G. Douglas, Steven Hurder, and Jerome Kaminker, Toeplitz operators and the eta invariant: the case of 𝑆¹, Index theory of elliptic operators, foliations, and operator algebras (New Orleans, LA/Indianapolis, IN, 1986) Contemp. Math., vol. 70, Amer. Math. Soc., Providence, RI, 1988, pp. 11–41. MR 948687, 10.1090/conm/070/948687
  • Ronald G. Douglas, Steven Hurder, and Jerome Kaminker, Toeplitz operators and the eta invariant: the case of 𝑆¹, Index theory of elliptic operators, foliations, and operator algebras (New Orleans, LA/Indianapolis, IN, 1986) Contemp. Math., vol. 70, Amer. Math. Soc., Providence, RI, 1988, pp. 11–41. MR 948687, 10.1090/conm/070/948687
  • R. G. Douglas, S. Hurder, and J. Kaminker, Cyclic cocycles, renormalization and eta-invariants, Invent. Math. 103 (1991), no. 1, 101–179. MR 1079841, 10.1007/BF01239510
  • Ronald G. Douglas, Steven Hurder, and Jerome Kaminker, The longitudinal cocycle and the index of Toeplitz operators, J. Funct. Anal. 101 (1991), no. 1, 120–144. MR 1132311, 10.1016/0022-1236(91)90151-T
  • [H1] S. Hurder, Eta-invariants and the index theorem for coverings, Univ. of III., Preprint, 1988.
  • [H 2] S. Hurder, Analysis and geometry of foliations, Research Monograph, Univ. of Colorado prepublication.
  • I. M. Singer, Some remarks on operator theory and index theory, 𝐾-theory and operator algebras (Proc. Conf., Univ. Georgia, Athens, Ga., 1975) Springer, Berlin, 1977, pp. 128–138. Lecture Notes in Math., Vol. 575. MR 0467848
  • I. M. Singer, Recent applications of index theory for elliptic operators, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 11–31. MR 0341538

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 58G10, 46L80, 57R30

Retrieve articles in all journals with MSC (1985): 58G10, 46L80, 57R30


Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1989-15769-8