On analytic torsion over C*-algebras

Alan Carey; Varghese Mathai; Alexander Mishchenko

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 43-67
  • ISSN: 0137-6934

Abstract

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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].

How to cite

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Carey, Alan, Mathai, Varghese, and Mishchenko, Alexander. "On analytic torsion over C*-algebras." Banach Center Publications 49.1 (1999): 43-67. <http://eudml.org/doc/208968>.

@article{Carey1999,
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].},
author = {Carey, Alan, Mathai, Varghese, Mishchenko, Alexander},
journal = {Banach Center Publications},
keywords = {analytic torsion; flat -algebra bundles; relative torsion},
language = {eng},
number = {1},
pages = {43-67},
title = {On analytic torsion over C*-algebras},
url = {http://eudml.org/doc/208968},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Carey, Alan
AU - Mathai, Varghese
AU - Mishchenko, Alexander
TI - On analytic torsion over C*-algebras
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 43
EP - 67
AB - 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].
LA - eng
KW - analytic torsion; flat -algebra bundles; relative torsion
UR - http://eudml.org/doc/208968
ER -

References

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  1. [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. Zbl0874.57025
  2. [2] A. L. Carey and V. Mathai, L 2 torsion invariants, J. Funct. Anal. 110 (1992), 377-409. 
  3. [3] J. Dodziuk, De Rham-Hodge theory for L 2 -cohomology of infinite coverings, Topology 16 (1977), 157-165. Zbl0348.58001
  4. [4] M. Gromov and M. Shubin, Von Neumann spectra near zero, Geom. Funct. Anal. 1 (1991), 375-404. Zbl0751.58039
  5. [5] J. Lott, Heat kernels on covering spaces and topological invariants, J. Diff. Geom. 35 (1992), 471-510. Zbl0770.58040
  6. [6] W. Luck and M. Rothenberg, Reidemeister torsion and the K-theory of von Neumann algebras, Math. Gott. Heft 31 (1991), 1-64. Zbl0748.57007
  7. [7] V. Mathai, L 2 analytic torsion, J. Funct. Anal. 107 (1992), 369-386; L 2 analytic torsion and locally symmetric spaces, preprint. 
  8. [8] W. Pashke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468. 
  9. [9] D. B. Ray and I. M. Singer, R-Torsion and the Laplacian on Riemannian manifolds, Adv. in Math. 7 (1971), 145-210. 
  10. [10] R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Appl. Math. 10 (1967), 288-388. Zbl0159.15504

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