2001/11/29 by Juergen Eichhorn, Eichhorn, Juergen
Mathematics · #58C40 #58J05 #58J20 #58J28 #58J35 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:58C40 #msc:58J05 #msc:58J20 #msc:58J28 #msc:58J35
paper · pdf · doi:10.48550/arxiv.math/0111301
arxiv created 2001/11/29 · openalex publication_date 2001/11/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 D2 has a gap above zero.