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A noncommutative geometric analysis of a sphere-torus topology change

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Journal publication date02/2004
JournalJournal of geometry and physics
Journal number2
Volume49
Number of pages20
Pages156-175
Original languageEnglish

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.