Connes’ Spin Manifold Theorem

Abstract

Let M be a compact oriented n-dimensional manifold without boundary. The theorem asserts that an n+-summable real geometry over the algebra C∞(M) determines a unique spin structure on M; and that, among all abstract spin geometries in the sense of Section 10.5, compatible with that structure, the one determined by the Dirac operator is singled out by a variational principle.KeywordsDirac OperatorVolume FormSpin StructurePseudodifferential OperatorSelfadjoint OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.