Curvature and Weitzenbock formulae for spectral triples

Differential Geometry Seminar

Organizers：

Jialong Deng, Akito Futaki

Speaker：

Bram Mesland（Universiteit Leiden)

Time：

Tues., 21:00-22:00

Oct. 15, 2024

Online：

Zoom Meeting ID: 271 534 5558

Passcode: YMSC

Title：

Curvature and Weitzenbock formulae for spectral triples

Abstract：

In this talk I will present a new, operator theoretic construction of the Levi-Civita connection on a Riemannian manifold, based on the two projection problem in Hilbert modules. The construction allows us to deduce the mild technical assumptions needed for the existence and uniqueness of the Levi-Civita connection on the module of differential 1-forms over a noncommutative algebra. In particular the construction applies to a large class of noncommutative manifolds (spectral triples). The well-known algebraic theory of curvature for bimodule connections can then be applied to derive a Weitzenbock formula. Examples include toric non commutative manifolds and the Podles quantum sphere. This is joint work with Adam Rennie.