Levi-Civita connections for a class of spectral triples.

Abstract: We give a new definition of Levi-Civita connection for a noncommutative pseudo-Riemannian metric on a noncommutative manifold given by a spectral triple. We prove the existence-uniqueness result for a class of modules of one-forms over a large class of noncommutative manifolds, including the matrix geometry of the fuzzy 3-sphere, the quantum Heisenberg manifolds and Connes-Landi deformations of spectral triples on the Connes-Dubois Violette-Rieffel-deformation of a compact manifold equipped with a free toral action. This is based on a joint work with J. Bhowmick and S. Mukhopadhyay.

general relativity and quantum cosmologyHEP - theorymathematical physicsquantum algebra

Audience: researchers in the topic

Mathematical Physics Seminar

Series comments: Description: Noncommutative geometry, field theory, gravity.