Examples in noncommutative localization

Examples of noncommutative instantons

These notes aim at a pedagogical introduction to recent work on deformation of spaces and deformation of vector bundles over them, which are relevant both in mathematics and in physics, notably monopole and instanton bundles. We first decribe toric noncommutative manifolds (also known as isospectral deformations). These come from deforming the usual Riemannian geometry of a manifold along a tor...

Noncommutative localization

The Teichmüller functor maps the category of elliptic curves over the field of characteristic zero to a category of the Effros-Shen algebras [9]. In the present note, we extend the functor to include the elliptic curves over the field of characteristic p. In particular, it is shown that the localization of a commutative ring at the maximal ideal corresponds to a crossed product of the Effros-Sh...

Limit Sets as Examples in Noncommutative Geometry

The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C∗-algebra. We construct nontrivial K-cycles for the cross-product algebra, thereby extending some results of Connes and Sullivan to higher dimensions. We also show how the Patterson-Sullivan measure on the limit set can be interpreted as a center-valued KMS state.

Noncommutative Finite-dimensional Manifolds I. Spherical Manifolds and Related Examples

We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete description of noncommutative three-dimensional spherical manifolds, a noncommutative version of the sphere S defined by basic K-theoretic equations. We find a 3-parameter family of deformations S u of the sta...

Three Examples of Gröbner Reduction over Noncommutative Rings