On analytic torsion over C*-algebras
Carey, Alan ; Mathai, Varghese ; Mishchenko, Alexander
Banach Center Publications, Tome 50 (1999), p. 43-67 / Harvested from The Polish Digital Mathematics Library
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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].

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:208968 
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     title = {On analytic torsion over C*-algebras},
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     volume = {50},
     year = {1999},
     pages = {43-67},
     zbl = {0941.19005},
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Carey, Alan; Mathai, Varghese; Mishchenko, Alexander. On analytic torsion over C*-algebras. Banach Center Publications, Tome 50 (1999) pp. 43-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p43bwm/

[000] [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. | Zbl 0874.57025

[001] [2] A. L. Carey and V. Mathai, L2 torsion invariants, J. Funct. Anal. 110 (1992), 377-409.

[002] [3] J. Dodziuk, De Rham-Hodge theory for L2-cohomology of infinite coverings, Topology 16 (1977), 157-165. | Zbl 0348.58001

[003] [4] M. Gromov and M. Shubin, Von Neumann spectra near zero, Geom. Funct. Anal. 1 (1991), 375-404. | Zbl 0751.58039

[004] [5] J. Lott, Heat kernels on covering spaces and topological invariants, J. Diff. Geom. 35 (1992), 471-510. | Zbl 0770.58040

[005] [6] W. Luck and M. Rothenberg, Reidemeister torsion and the K-theory of von Neumann algebras, Math. Gott. Heft 31 (1991), 1-64. | Zbl 0748.57007

[006] [7] V. Mathai, L2 analytic torsion, J. Funct. Anal. 107 (1992), 369-386; L2 analytic torsion and locally symmetric spaces, preprint.

[007] [8] W. Pashke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468.

[008] [9] D. B. Ray and I. M. Singer, R-Torsion and the Laplacian on Riemannian manifolds, Adv. in Math. 7 (1971), 145-210.

[009] [10] R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Appl. Math. 10 (1967), 288-388. | Zbl 0159.15504