### 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) |
---|---|

Pages (from-to) | 31-91 |

Number of pages | 61 |

Journal | Mathematische Nachrichten |

Volume | 208 |

State | Published - 1999 |

### Fingerprint

### Keywords

- Glueing formulas
- Manifolds with boundaries
- Torsions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Nachrichten*,

*208*, 31-91.

**Torsions for manifolds with boundary and glueing formulas.** / Burghelea, Dan; Friedlander, Leonid; Kappeler, Thomas.

Research output: Contribution to journal › Article

*Mathematische Nachrichten*, vol. 208, pp. 31-91.

}

TY - JOUR

T1 - Torsions for manifolds with boundary and glueing formulas

AU - Burghelea, Dan

AU - Friedlander, Leonid

AU - Kappeler, Thomas

PY - 1999

Y1 - 1999

N2 - 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 L2-analytic resp. L2-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).

AB - 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 L2-analytic resp. L2-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).

KW - Glueing formulas

KW - Manifolds with boundaries

KW - Torsions

UR - http://www.scopus.com/inward/record.url?scp=0008292459&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008292459&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0008292459

VL - 208

SP - 31

EP - 91

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

ER -