A Noncommutative Geometric Analysis of a Sphere/Torus Topology Change

Details A Noncommutative Geometric Analysis of a Sphere/Torus Topology Change A Noncommutative Geometric Analysis of a Sphere/Torus Topology Change

2003-04-27

arxiv.org/abs/math/0304427v1

J Geometry Physics 49 (2004) 156-175

Mathematics

Quantum Algebra

18 pages. 16 small eps figures. To be printed in Journal of Geometry and Physics

Scientific paper

10.1016/S0393-0440(03)00072-X

A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or variety. The topology of the manifold or variety depends on the parameter, varying from nothing, to a point, a sphere, a certain variety and finally a torus. The irreducible adjoint preserving representations of the noncommutative algebras are studied. As well as typical noncommutative sphere type representations and noncommutative torus type representations, a new object is discovered and called a Sphere-Torus.

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