Conformal structures in noncommutative geometry

Abstract

It is well known that a compact Riemannian spin manifold (M, g) can be reconstructed from its canonical spectral triple (C∞(M), L2(M,ΣM), D) where ΣM denotes the spinor bundle and D the Dirac operator. We show that g can be reconstructed up to conformal equivalence from (C∞(M), L2(M,ΣM), sign(D)).