A noncommutative geometric analysis of a sphere-torus topology change

Gratus, J (2004) A noncommutative geometric analysis of a sphere-torus topology change. Journal of Geometry and Physics, 49 (2). pp. 156-175. ISSN 0393-0440

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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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Journal Article
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Journal of Geometry and Physics
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10 Jan 2012 11:36
Last Modified:
21 Nov 2022 22:00