1. P. Olczykowski, A.Sitarz
K-theory of noncommutative Bieberbach manifolds,
(2012).
[abstract] [preprint]

Abstract:
We compute K-theory of noncommutative Bieberbach manifolds, which quotients of a three-dimensional noncommutative torus by a free action of a cyclic group Z_N, N = 2; 3; 4; 6.

2. P. Olczykowski, A. Sitarz
On spectral action over Bieberbach manifolds
Acta Phys. Pol., B , vol. 42, p. 1189 (2011).
[abstract] [preprint] [journal] [download]

Abstract:
We compute the leading terms of the spectral action for orientable three dimensional Bieberbach manifolds using two different methods: the Poisson summation formula and the perturbative expansion. Assuming that the cut-off function is not necessarily symmetric we find that the scale invariant part of the perturbative expansion might only differ from the spectral action of the flat three-torus by the value of the eta invariant.