Essentially commutative C*-algebras with essential spectrum homeomorphic to S2n-1

This paper gives a complete classification of essentially commutative C*-al gebras whose essential spectrum is homeomorphic to S2n-1 by their character istic numbers. Let A(1), A(2) be such two C*-algebras; then they are C*-iso morphic if and only if they have the same n-th characteristic number. Furth ermore, Let gamma (n)(A) = m; then A is C*-isomorphic to C*(M-zn,..., M-zn) if m = 0, A is C*-isomorphic to C*(T-z1,..., Tzn-1, T-zn(m)) if m not equa l 0, Some examples are given to show applications of the classification the orem. We finally remark that the proof of the theorem depends on a construc tion of a complete system of representatives of Ext(S2n-1).