0 D ec 2 01 5 NONCOMMUTATIVE LINE BUNDLES ASSOCIATED TO TWISTED MULTIPULLBACK QUANTUM ODD SPHERES

We construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2N + 1)-dimensional sphere into (N + 1)many solid tori. This generalizes the case N = 1 referred to as the Heegaard quantum sphere. Our twisted odd-dimensional quantum sphere C∗-algebras are given as multipullback C∗-algebras. We prove that they are isomorphic to the universal C∗-algebras generated by certain isometries, and use this result to compute the K-groups of our odd-dimensional quantum spheres. Furthermore, we show that the natural (diagonal) U(1)-actions on our twisted-quantum-sphere C∗-algebras are C∗-free, and define twisted multipullback quantum complex projective spaces through fixed-point subalgebras for these actions. In the untwisted case, we prove that the fixed-point subalgebras yield the independently defined C∗-algebras of the quantum complex projective spaces constructed from Toeplitz cubes. This leads to the main result stating that the noncommutative line bundles associated to multipullback quantum odd spheres, which are noncommutative line bundles over these quantum complex projective spaces, are pairwise stably nonisomorphic.