THE FREE COVER OF A ROW CONTRACTION
Abstract. We establish the existence and uniqueness of finite free res-
olutions - and their attendant Betti numbers - for graded commuting
d-tuples of Hilbert space operators. Our approach is based on the no-
tion of free cover of a (perhaps noncommutative) row contraction. Free
covers provide a flexible replacement for minimal dilations that is bett*
suited for higher-dimensional operator theory.
For example, every graded d-contraction that is finitely multi-cyclic