The K-theory of heegaard-type quantum 3-spheres

Paul F. Baum; Piotr M. Hajac; Rainer Matthes; Wojciech Szymański

doi:10.1007/s10977-005-1550-y

The K-theory of heegaard-type quantum 3-spheres

Paul F. Baum, Piotr M. Hajac, Rainer Matthes, Wojciech Szymański

Mathematics

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19 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	159-186
Number of pages	28
Journal	K-Theory
Volume	35
Issue number	1-2
DOIs	https://doi.org/10.1007/s10977-005-1550-y
State	Published - Jun 2005

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s10977-005-1550-y

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abstract = "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.",

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N2 - 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.

AB - 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.

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The K-theory of heegaard-type quantum 3-spheres

Abstract

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