### Abstract

We extend the definition of analytic and Reidemeister torsion for closed compact Riemannian manifolds, to compact Riemannian manifolds with boundary (M, ∂M), given a parallel flat bundle F of A - Hilbert modules of finite type and a decomposition of the boundary ∂M = ∂_M ∪∂_{+}M into disjoint components. When F is induced from the universal covering of M, and the fundamental group of M is infinite (cf. [BFKM]), these torsions are known as the L_{2}-analytic resp. L_{2}-Reidemeister torsions. If the system (M, ∂_M, ∂_{+}M,F) is of determinant class we compute the quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of them. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ principal covering where Γ is a residually finite group, we derive from work of LÜCK (cf. [L3]), that, the system (M, ∂_M, ∂_{+}M, F) is of determinant class (cf. Theorem 5.1 in Appendix A).

Original language | English (US) |
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Pages (from-to) | 31-91 |

Number of pages | 61 |

Journal | Mathematische Nachrichten |

Volume | 208 |

DOIs | |

State | Published - 1999 |

### Keywords

- Glueing formulas
- Manifolds with boundaries
- Torsions

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Mathematische Nachrichten*,

*208*, 31-91. https://doi.org/10.1002/mana.3212080103