The geometry of determinant line bundles in noncommutative geometry
  This paper is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalent classes of Hermitian connections on a Hermitian finite projective module. We illustrate our results with some examples that arise in noncommutative geometry. 
Partha Sarathi Chakraborty, Varghese Mathai