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

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

2001-11-29

arxiv.org/abs/math/0111301v1

Mathematics

Differential Geometry

Scientific paper

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 $\gencomp (E)$ 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 $\zeta$-- and $\eta$--functions, relative determinants and in the case of $D=\Delta$ relative analytic torsion. To define relative $\zeta$-- and $\eta$--functions, we assume additionally that the essential spectrum of $D^2$ has a gap above zero.

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