Torsions for manifolds with boundary and glueing formulas

We extend the definition of analytic and Reidemeister torsion for closed co mpact Riemannian manifolds, to compact Riemannian manifolds with boundary ( M, partial derivative M), given a parallel flat bundle F of A-Hilbert modul es of finite type and a decomposition of the boundary partial derivative M = partial derivative(-)M boolean OR partial derivative(+)M into disjoint co mponents. When F is induced from the universal covering of M, and the funda mental 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,partial der ivative(-)M,partial derivative(+)M,F) is of determinant class we compute th e quotient of the analytic and the Reidemeister torsion and prove: gluing f ormulas for both of them. In particular we answer positively Conjecture 7.6 in [LL]. If 3 is induced from a Gamma-principal covering where Gamma is a residually finite group, we derive from work of LUCK (cf. [L3]), that the s ystem (M, partial derivative(-)M,partial derivative(+)M,F) is of determinan t class (cf. Theorem 5.1 in Appendix A).