For a closed Riemannian manifold (M, g) we extend the definition of analytic and Reidemeister torsion associated to a unitary representation of π₁(M) on a finite dimensional vector space to a representation on a A-Hilbert module W of finite type where A is a finite von Neumann algebra. If (M,W) is of determinant class we prove, generalizing the Cheeger-Müller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L₂-analytic and L₂-Reidemeister torsions are equal.

Burghelea, D; Friedlander, L; Kappeler, T; McDonald, P (1996). *Analytic and Reidemeister torsion for representations in finite type Hilbert modules.* Geometric and Functional Analysis, 6(5):751-859.

## Abstract

For a closed Riemannian manifold (M, g) we extend the definition of analytic and Reidemeister torsion associated to a unitary representation of π₁(M) on a finite dimensional vector space to a representation on a A-Hilbert module W of finite type where A is a finite von Neumann algebra. If (M,W) is of determinant class we prove, generalizing the Cheeger-Müller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L₂-analytic and L₂-Reidemeister torsions are equal.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 1996 |

Deposited On: | 29 Nov 2010 16:28 |

Last Modified: | 05 Apr 2016 13:27 |

Publisher: | Birkhäuser |

ISSN: | 1016-443X |

Free access at: | Related URL. An embargo period may apply. |

Publisher DOI: | https://doi.org/10.1007/BF02246786 |

Related URLs: | http://www.digizeitschriften.de/dms/img/?PPN=PPN359089402_0006&DMDID=dmdlog38 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0874.57025 |

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