Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Inequalities for the Novikov-Shubin invariants

Author: Varghese Mathai
Journal: Proc. Amer. Math. Soc. 124 (1996), 2585-2588
MSC (1991): Primary 58G11, 58G18, 58G25
MathSciNet review: 1328361
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove that the Novikov-Shubin invariants satisfy a sequence of inequalities and deduce some useful consequences of this result.

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

  • 1. 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
  • 2. Alan L. Carey and Varghese Mathai, 𝐿²-torsion invariants, J. Funct. Anal. 110 (1992), no. 2, 377–409. MR 1194991, 10.1016/0022-1236(92)90036-I
  • 3. A. V. Efremov, Cell decompositions and the Novikov-Shubin invariants, Uspekhi Mat. Nauk 46 (1991), no. 3(279), 189–190 (Russian); English transl., Russian Math. Surveys 46 (1991), no. 3, 219–220. MR 1134099, 10.1070/RM1991v046n03ABEH002800
  • 4. D. V. Efremov and M. A. Shubin, Spectrum distribution function and variational principle for automorphic operators on hyperbolic space, Séminaire sur les Équations aux Dérivées Partielles, 1988–1989, École Polytech., Palaiseau, 1989, pp. Exp. No. VIII, 19. MR 1032284
  • 5. M. Gromov and M. A. Shubin, von Neumann spectra near zero, Geom. Funct. Anal. 1 (1991), no. 4, 375–404. MR 1132295, 10.1007/BF01895640
  • 6. John Lott, Heat kernels on covering spaces and topological invariants, J. Differential Geom. 35 (1992), no. 2, 471–510. MR 1158345
  • 7. J. Lott and W. Lück, $L^{2}$ topological invariants of 3-manifolds, (to appear in Inven. Math.).
  • 8. Wolfgang Lück and Mel Rothenberg, Reidemeister torsion and the 𝐾-theory of von Neumann algebras, 𝐾-Theory 5 (1991), no. 3, 213–264. MR 1162441, 10.1007/BF00533588
  • 9. Varghese Mathai, 𝐿²-analytic torsion, J. Funct. Anal. 107 (1992), no. 2, 369–386. MR 1172031, 10.1016/0022-1236(92)90114-X
  • 10. V. Mathai, $L^2$ analytic torsion and locally symmetric spaces, preprint 1991.
  • 11. V. Mathai and S. Weinberger, Shifted $L^2$ Invariants and Amenable manifolds, preprint 1994.
  • 12. John Roe, Elliptic operators, topology and asymptotic methods, Pitman Research Notes in Mathematics Series, vol. 179, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. MR 960889

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58G11, 58G18, 58G25

Retrieve articles in all journals with MSC (1991): 58G11, 58G18, 58G25

Additional Information

Varghese Mathai
Affiliation: Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia, Australia

Keywords: Heat kernels, Novikov-Shubin invariants, positive decay
Received by editor(s): February 15, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society