The Noncommutative Geometry Generalization of Fundamental Group
  A notion of fundamental group of spectral triples has been introduced. The notion uses a noncommutative analogue of unramified coverings. It was shown that in commutative case this fundamental group is a profinite completion of fundamental group of corresponding Riemann manifold. 
Petr R. Ivankov and Nickolay P. Ivankov