Abstract

Representing Z/NZ as roots of unity, we restrict a natural U(1)action on the
Heegaard quantum sphere to Z/NZ, and call the quotient spaces Heegaard quantum lens spaces.
Then we use this representation of Z/NZ to construct an associated complex line bundle. This
paper proves the stable nontriviality of these line bundles over any of the quantum lens spaces
we consider. We use the pullback structure of the C∗algebra of the lens space to compute
its Ktheory via the MayerVietoris sequence, and an explicit form of the Bass connecting
homomorphism to prove the stable nontriviality of the bundles. On the algebraic side we
prove the universality of the coordinate algebra of such a lens space for a particular set of
generators and relations. We also prove the nonexistence of nontrivial invertibles in the
coordinate algebra of a lens space. Finally, we prolongate the Z/NZfibres of the Heegaard
quantum sphere to U(1), and determine the algebraic structure of such a U(1)prolongation.