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The \(K\)-theory of Heegaard-type quantum 3-spheres. (English) Zbl 1111.46051
\(K\)-Theory 35, No. 1-2, 159-186 (2005); erratum ibid. 37, No. 1-2, 211 (2006).
Summary: We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative deformations. The main technical point is an identification of the universal \(C^{*}\)-algebras defining our quantum 3-spheres with an appropriate fiber product of crossed-product \(C^{*}\)-algebras. Then we employ this result to show that the \(K\)-groups of our family of noncommutative 3-spheres coincide with their classical counterparts.

MSC:
46L87 Noncommutative differential geometry
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