# 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

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topCarey, 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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- [7] V. Mathai, ${L}^{2}$ analytic torsion, J. Funct. Anal. 107 (1992), 369-386; ${L}^{2}$ 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.
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