  Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The
fixed point algebras, termed quantum weighted Heegaard spheres, and their
representations are classified and described on algebraic and topological
levels. On the algebraic side, coordinate algebras of quantum weighted Heegaard
spheres are interpreted as generalised Weyl algebras, quantum principal circle
bundles and Fredholm modules over them are constructed, and the associated line
bundles are shown to be non-trivial by an explicit calculation of their Chern
numbers. On the topological side, the C*-algebras of continuous functions on
quantum weighted Heegaard spheres are described and their K-groups are
calculated.
