Conformal Structures in Noncommutative Geometry

Abstract

It is well-known that a compact Riemannian spin manifold can be reconstructed from its canonical spectral triple which consists of the algebra of smooth functions, the Hilbert space of square integrable spinors and the Dirac operator. It seems to be a folklore fact that the metric can be reconstructed up to conformal equivalence if one replaces the Dirac operator D by sign(D). We give a precise formulation and proof of this fact.

8 pages, published version

References in corpus (1)

• General Relativity in terms of Dirac Eigenvalues

Cited by in corpus (2)

• Zeta functions that hear the shape of a Riemann surface
• Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary