Lifting spectral triples to noncommutative principal bundles

Abstract

Given a free action of a compact Lie group $G$ on a unital C*-algebra $\mathcal{A}$ and a spectral triple on the corresponding fixed point algebra ${\mathcal{A}}^G$, we present a systematic and in-depth construction of a spectral triple on $\mathcal{A}$ that is build upon the geometry of ${\mathcal{A}}^G$ and $G$. We compare our construction with a selection of established examples.

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• A Note on Twisted Crossed Products and Spectral Triples
• An Atiyah Sequence for Noncommutative Principal Bundles
• Realizations of free actions via their fixed point algebras