  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.
