Metric-compatible connections in noncommutative geometry

Abstract: Levi-Civita's theorem in Riemannian geometry states that if $(M, g)$ is a Riemannian manifold, then there exists a unique connection on $M$ which is torsionless and compatible with $g$. The curvature of the manifold is then computed from this particular connection.

We will try to explain the notions to state and prove Levi-Civita's theorem in the context of a noncommutative differential calculus. In particular, we will describe two notions of metric-compatibility of a connection. The talk will be based on joint works with D. Goswami, S. Joardar, G. Landi and S. Mukhopadhyay.

The geometric notions appearing in the lecture will be defined and explained in the beginning.

functional analysisoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras