SPECTRAL TRIPLES FOR NONCOMMUTATIVE SOLENOIDS

Noncommutative solenoids are inductive limit algebras built from rotation algebras. By viewing noncommutative solenoids as twisted group C*-algebras, we construct odd finitely summable spectral triples for noncommutative solenoids based on length functions of bounded doubling. Our spectral triples also induce a Leibniz quantum compact metric space structure.  In addition, our spectral triples for noncommutative solenoids are, in the sense of Floricel and Ghorbanpour, likewise inductive limits of spectral triples on rotation algebras. Furthermore, our odd spectral triples can be defined to have an associated smooth dense subalgebra which is stable under the holomorphic functional calculus, thereby answering a question of B. Long and W. Wu. This is joint work with C. Farsi, N. Larsen, and J. Packer.