Let be a length function on a discrete abelian group Let be a multiplier on (two cocycle taking values in Rieffel and collaborators, following work of Connes, have used to construct a ``Dirac" operator on giving spectral triples with for the twisted group -algebra mostly when is finitely generated Following Rieffel's work and recent work of Long and Wu, we construct odd spectral triples for noncommutative solenoids first studied by the author and Latremoliere. The Dirac operator involved can be used to construct a metric on the state space of the twisted group -algebra, which induces a topology coinciding with the weak- topology.
This talk is based on joint work with C. Farsi, T. Landry and N. Larsen.