The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral ζ-invariants using lifted defect formulae which express discrepancies of ζ-regularised traces in terms of Wodzicki residues. We derive Atiyah’s L2-index theorem as an instance of the Z2-graded generalisation of the canonical lift of spectral ζinvariants and we show that certain lifted spectral ζ-invariants for geometric operators are integrals of Pontryagin and Chern forms.
SPECTRAL ζ-INVARIANTS LIFTED to COVERINGS
Azzali S.;
2020-01-01
Abstract
The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral ζ-invariants using lifted defect formulae which express discrepancies of ζ-regularised traces in terms of Wodzicki residues. We derive Atiyah’s L2-index theorem as an instance of the Z2-graded generalisation of the canonical lift of spectral ζinvariants and we show that certain lifted spectral ζ-invariants for geometric operators are integrals of Pontryagin and Chern forms.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
