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)).
Cite this article
Christian Bär, Conformal structures in noncommutative geometry. J. Noncommut. Geom. 1 (2007), no. 3, pp. 385–395DOI 10.4171/JNCG/11