Topology Change and Vector Modules on Noncommutative Surfaces of Rotation

Abstract

A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent spaces in noncommutative geometry, via the definition of an exterior derivative. This derivative reduces to the standard exterior derivative in the commutative limit. The representation of this algebra is used to investigate a simple topology change where two connected compact surfaces coalesce to form one such surface.