Dirac operators on noncommutative hypersurfaces

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a noncommutative embedding space to a noncommutative hypersurface is developed and applied to obtain noncommutative hypersurface Dirac operators. The general construction is illustrated by studying the sequence $\mathbb{T}^{2}_θ \hookrightarrow \mathbb{S}^{3}_θ \hookrightarrow \mathbb{R}^{4}_θ$ of noncommutative hypersurface embeddings.

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