Journal of Noncommutative Geometry

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Volume 1, Issue 3, 2007, pp. 385–395
DOI: 10.4171/JNCG/11

Published online: 2007-09-30

Conformal structures in noncommutative geometry

Christian Bär[1]

(1) University of Potsdam, Germany

It is well known that a compact Riemannian spin manifold (M, g) can be reconstructed from its canonical spectral triple (C(M), L2(MM), 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(MM), sign(D)).

Keywords: Fredholm module, spectral triple, Dirac operator, conformally equivalent Riemannian metrics

Bär Christian: Conformal structures in noncommutative geometry. J. Noncommut. Geom. 1 (2007), 385-395. doi: 10.4171/JNCG/11