PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson, Stephanie Zerby.

Title:Odd-dimensional multi-pullback quantum spheres
Seminar:Noncommutative Geometry Seminar
Speaker:Piotr Hajac, Polish Academy of Sciences
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 odd-dimensional quantum sphere C*-algebras are given as multi-pullback 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 prove that the fixed-point subalgebras under the diagonal U(1)-action on our quantum sphere C*-algebras yield the independently defined C*-algebras of the quantum complex projective spaces constructed from the Toeplitz cubes. Then, by constructing a strong connection, we show that this U(1)-action is free. This leads to the main result stating that the noncommutative line bundles over the quantum complex projective spaces that are associated to this action via non-trivial representations of U(1) are not stably trivial. (Based on joint work with D. Pask, A. Sims and B. ZieliƄski.)

Room Reservation Information

Room Number:MB106
Date:02 / 05 / 2015
Time:02:30pm - 03:30pm