On the spectral characterization of manifolds | Zendy

Alain Connes | Zendy

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On the spectral characterization of manifolds

Author(s) -

Alain Connes

Publication year - 2013

Publication title -

journal of noncommutative geometry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.037

H-Index - 26

eISSN - 1661-6960

pISSN - 1661-6952

DOI - 10.4171/jncg/108

Subject(s) - mathematics , spectral triple , characterization (materials science) , pure mathematics , axiom , spectral asymmetry , manifold (fluid mechanics) , metric (unit) , commutative property , dirac operator , riemannian manifold , type (biology) , algebra over a field , noncommutative geometry , dirac algebra , dirac equation , geometry , economics , mathematical physics , mechanical engineering , operations management , materials science , noncommutative quantum field theory , engineering , nanotechnology , ecology , biology

We show that the first five of the axioms we had formulated on spectraltriples suffice (in a slightly stronger form) to characterize the spectraltriples associated to smooth compact manifolds. The algebra, which is assumedto be commutative, is shown to be isomorphic to the algebra of all smoothfunctions on a unique smooth oriented compact manifold, while the operator isshown to be of Dirac type and the metric to be Riemannian.

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