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orsions for Manifolds with Boundary and Glueing Formulas
Author(s) -
Burghelea Dan,
Friedlander Leonid,
Kappeler Thomas
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3212080103
Subject(s) - mathematics , quotient , torsion (gastropod) , pure mathematics , conjecture , fundamental group , boundary (topology) , disjoint sets , holonomy , cohomology , combinatorics , mathematical analysis , medicine , surgery
We extend the definition of analytic and Reidemeister torsion for closed compact iemannian manifolds, to compact Riemannian manifolds with boundary ( M , δ M ), given a parallel at bundle F of A ‐Hilbert modules of finite type and a decomposition of the boundary δ M = ‐ M ⊔ δ+ 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. 2 ‐Reidemeister torsions. If the system ( M, δ‐M, δ+M, F ) is of determinant class we compute he quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of hem. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ‐principal overing where Γ is a residually finite group, we derive from work of Lück (cf. [L3]), that the system ( M, δ‐M, δ+M, F ) is of determinant class (cf. Theorem 5.1 in Appendix A).