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A noncommutative geometric analysis of a sphere-torus topology change

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<mark>Journal publication date</mark>02/2004
<mark>Journal</mark>Journal of Geometry and Physics
Issue2
Volume49
Number of pages20
Pages156-175
<mark>Original language</mark>English

Abstract

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.