The Levi-Civita connection on noncommutative differential forms

Adam Rennie (University of Wollongong)

Thursday 11th April 16:00-17:00 Maths 116


By combining Hilbert module and algebraic techniques,we give necessary and sufficient conditions for the existence of Hermitian and torsion-free connections on noncommutative one-forms, such as those arising from spectral triples. With additional structure we give a sufficient condition for uniqueness.

Our methods are constructive, use standard definitions, and allow computation of curvature with comparable difficulty to the differential geometry case.
Joint work with Bram Mesland.

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