Noncommutative Geometry and Geometric Structures

• Applicant: Professor Dr. Christian Bär
• Subject Area: Mathematics
• Term: from 2003 to 2005
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5406976

In a fundamental paper Rennie claims to characterize closed Riemannian spin manifolds as spectral triples with a commutative C*-algebra plus some additional algebraic data. Firstly, the status of this result has to be clarified. Secondly, versions for manifolds with additional geometric structure are to be characterized. Moreover, compact manifolds with additional geometric structure (e.g. Kähler metrics or, more generally, metrics with restricted holonomy) are to be characterized. Moreover, compact manifolds with boundary and suitable noncompact manifolds should be incorporated. Finally, one will try to pass from the Riemannian to the Lorentzian case.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry