A DEGREE FORMULA FOR EQUIVARIANT COHOMOLOGY RINGS

This paper generalizes a result of Lynn on the "degree" of an equivariant cohomology ring H*G(X). The degree of a graded module is a certain coefficient of its Poincare & PRIME; series, and is closely related to multiplicity. In the present paper, we study these commutative algebraic invariants for equivariant cohomol-ogy rings. The main theorem is an additivity formula for degree: � deg(H* G(X)) = [A,c]& ISIN;Q & PRIME;max(G,X) 1 |WG(A,c)|deg(H*CG(A,c)(c)). We also show how this formula relates to the additivity formula from commutative algebra, demonstrating both the algebraic and geometric character of the degree invariant.