# Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples

@article{Connes2001NoncommutativeFM, title={Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples}, author={Alain Connes and Michel Dubois-Violette}, journal={Communications in Mathematical Physics}, year={2001}, volume={230}, pages={539-579} }

Abstract: We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete description of noncommutative three-dimensional spherical manifolds, a noncommutative version of the sphere S3 defined by basic K-theoretic equations. We find a 3-parameter family of deformations of the standard 3-sphere S3 and a corresponding 3-parameter deformation of the 4-dimensional Euclidean…

## 259 Citations

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