Relative Zeta Functions, Determinants, Torsion, Index Theorems and Invariants for Open Manifolds

The set of Clifford bundles of bounded geometry over open manifolds can be endowed with a metrizable uniform structure. For one fixed bundle E we define the generalized component gen comp(E) as the set of Clifford bundles E′ which have finite distance to E. If D, D′ are the associated generalized Dirac operators, we prove for the pair (D,D′) relative index theorems, define relative ζ– and η– functions, relative determinants and in the case of D = ∆ relative analytic torsion. To define relative ζ– and η–functions, we assume additionally that the essential spectrum of D2 has a gap above zero.