Torsions for manifolds with boundary and glueing formulas

Burghelea, D.; Friedlander, L.; Kappeler, T.

Torsions for manifolds with boundary and glueing formulas

Authors

Burghelea, D.

Friedlander, L.

Kappeler, T.

Description

We extend the definition of analytic and Reidemeister torsion from closed compact Riemannian manifolds to compact Riemannian manifolds with boundary $(M, \partial M)$, given a flat bundle $\Cal F$ of $\Cal A$-Hilbert modules of finite type and a decomposition of the boundary $\partial M =\partial_- M \cup \partial_+ M$ into disjoint components. In particular we extend the $L-2$ analytic and Reidemeister torsions to compact manifolds with boundary. If the system $(M,\partial_-M, \partial_+M, \Cal F)$ is of determinant class we compute the quotient of the analytic and the Reidemeister torsion and prove glueing formulas for both of them. In particular we answer positively Conjecture 7.6 in [LL]
58 pages, amstex