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}{\theta} \hookrightarrow $\mathbb{S}$^{3}{\theta} \hookrightarrow $\mathbb{R}$^{4}_{\theta}$ of noncommutative hypersurface embeddings.