A degree formula for equivariant cohomology (Q2862132)

The author relates some algebraic computations of multiplicity from commutative algebra to computations done in the cohomology theory of group actions on manifolds. \textit{D. Quillen}'s results [Ann. Math. (2) 94, 549--572, 573--602 (1971; Zbl 0247.57013)] are used and the cohomology ring \(H^\ast_G(X)=H^\ast(EG\times_GX,\mathbb{Z}_p)\) of the Borel construction \(EG\times_GX\) for a \(G\)-manifold \(X\) is applied to compute the degree NEWLINE\[NEWLINE\text{deg}(H^\ast_G(X)))=\lim_{t\to 1}(1-t)^{D(H^\ast_G(X))}PS(H^\ast_G(X),t)NEWLINE\]NEWLINE via the Poincaré series \(PS(H^\ast_G(X),t)\).NEWLINENEWLINEA formula that computes the ``degree'' of the Poincaré series in terms of corresponding degrees of certain subgroups of a finite group \(G\) is presented.