Noncommutative Differential Geometry and Its Applications to Physics

Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments.
However, noncommutative differential geometry was not well understood even among ...