TL;DR
This paper explores the properties of fuzzy surfaces of genus zero, focusing on linear connections and their dependence on differential calculus, with a specific emphasis on perturbations of the fuzzy sphere.
Contribution
It introduces a study of linear connections on fuzzy genus zero surfaces, highlighting their dependence on differential calculus and constructing various non-covariant examples.
Findings
Linear connections depend on the differential calculus used.
Many non-covariant differential calculi can be constructed.
Analysis limited to small perturbations of the fuzzy sphere.
Abstract
A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly dependent on the differential calculus used but that a large number of the latter can be constructed which are not covariant under the action of the rotation group. For technical reasons we have been forced to limit our considerations to fuzzy surfaces which are small perturbations of the fuzzy sphere.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.