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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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##### References:
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