  Some time ago we presented an article (which was in fact the outline of a
research programme) in which we argued for the need to develop a nonommutative
version of topological quantum field theories (NCTQFT for short). Recent work
by C.J. Hogan et all, has demonstrated the possibility to get experimental
verification of holography; if this comes true, then that would indicate that
quantum gravity is indeed a TQFT. On the other hand there is accumulating
evidence that the underlying geometry of spacetime is a noncommutative
(abreviated to nc in the sequel) space, hence if one wants a unified theory of
all physical interactions including gravity that would mean that the right
framework would be NCTQFT. Towards this goal we present a modest achievement
which is a nc version of Hodge Theorem and the definition of the nc free
bosonic propagator.
