ArticleOriginal scientific text

Title

On analytic torsion over C*-algebras

Authors 1, 1, 2

Affiliations

  1. Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia
  2. Department of Mathematics, Moscow State University, 117 234 Moscow, Russia

Abstract

In this paper, we present an analytic definition for the relative torsion for flat C*-algebra bundles over a compact manifold. The advantage of such a relative torsion is that it is defined without any hypotheses on the flat C*-algebra bundle. In the case where the flat C*-algebra bundle is of determinant class, we relate it easily to the L^2 torsion as defined in [7],[5].

Bibliography

  1. D. Burghelea, L. Friedlander, T. Kappeler and P. McDonald, Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Geom. Funct. Anal. 6 (1996), 751-859.
  2. A. L. Carey and V. Mathai, L2 torsion invariants, J. Funct. Anal. 110 (1992), 377-409.
  3. J. Dodziuk, De Rham-Hodge theory for L2-cohomology of infinite coverings, Topology 16 (1977), 157-165.
  4. M. Gromov and M. Shubin, Von Neumann spectra near zero, Geom. Funct. Anal. 1 (1991), 375-404.
  5. J. Lott, Heat kernels on covering spaces and topological invariants, J. Diff. Geom. 35 (1992), 471-510.
  6. W. Luck and M. Rothenberg, Reidemeister torsion and the K-theory of von Neumann algebras, Math. Gott. Heft 31 (1991), 1-64.
  7. V. Mathai, L2 analytic torsion, J. Funct. Anal. 107 (1992), 369-386; L2 analytic torsion and locally symmetric spaces, preprint.
  8. W. Pashke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468.
  9. D. B. Ray and I. M. Singer, R-Torsion and the Laplacian on Riemannian manifolds, Adv. in Math. 7 (1971), 145-210.
  10. R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Appl. Math. 10 (1967), 288-388.
Pages:
43-67
Main language of publication
English
Published
1999
Exact and natural sciences