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

Juergen Eichhorn
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Abstract

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 $ζ$-- and $η$--functions, relative determinants and in the case of $D=Δ$ relative analytic torsion. To define relative $ζ$-- and $η$--functions, we assume additionally that the essential spectrum of $D^2$ has a gap above zero.

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BibTeXRIS

Juergen Eichhorn. 2001-11-29. Relative Zeta Functions, Determinants, Torsion, Index Theorems and Invariants for Open Manifolds. https://arxiv.org/abs/math/0111301

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