Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the Heegaard quantum 3-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. The main result is the stable non-triviality 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 K-theory via the Mayer-Vietoris six-term exact sequence. Then we combine an explicit form of the odd-to-even connecting homomorphism (Milnor idempotent) with Chern-Galois theory (strong connections) to prove the stable non-triviality of the bundles. (Joint work with Adam Rennie and Bartosz Zielinski.)
THE K-THEORY OF HEEGAARD QUANTUM LENS SPACES Sponsored by the Meyer Fund
THE K-THEORY OF HEEGAARD QUANTUM LENS SPACES