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.
