The K-Theory of Heegaard-Type Quantum 3-Spheres
  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. 
Paul Baum, Piotr M. Hajac, Rainer Matthes, Wojciech Szymanski