K-theory, cyclic cohomology and pairings for quantum Heisenberg manifolds

The C*-algebras called Quantum Heisenberg Manifolds (QHM) were introduced byRieffel in 1989 as strict deformation quantizations of Heisenberg manifolds. Inthis article, we compute the pairings of K-theory and cyclic cohomology on theQHM. Combining these calculations with other results proved elsewhere, we alsodetermine the periodic cyclic homology and cohomology of these algebras, andobtain explicit bases of the periodic cyclic cohomology of the QHM. We furtherisolate bases of periodic cyclic homology, expressed as Chern characters of theK-theory.