  The approach we present is a modification of the Morse theory for unital
C*-algebras. We provide tools for the geometric interpretation of
noncommutative CW complexes. These objects were introduced and studied in
[2],[7] and [14]. Some examples to illustrate these geometric information in
practice are given. A classification of unital C*-algebras by noncommutative CW
complexes and the modified Morse functions on them is the main object of this
work.
