Geodesic
A degree formula for equivariant cohomology rings
Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 345-365.

Voir la notice de l'article provenant de la source International Press of Boston

This paper generalizes a result of Lynn on the “degree” of an equivariant cohomology ring H^\ast_G (X). The degree of a graded module is a certain coefficient of its Poincaré series, and is closely related to multiplicity. In the present paper, we study these commutative algebraic invariants for equivariant cohomology rings. The main theorem is an additivity formula for degree:\[\deg (H^\ast_G (X)) =\sum_{[A,c] \in \mathcal{Q}^\prime _{\:\max \:} (G,X)}\dfrac{1}{\lvert W_g (A,c) \rvert}\deg(H^\ast_{C_g (A,c)} (c)) \; \textrm{.}\]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.
DOI : 10.4310/HHA.2023.v25.n1.a18
Keywords: homology, homotopy 
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Mark Blumstein; Jeanne Duflot. A degree formula for equivariant cohomology rings. Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 345-365. doi : 10.4310/HHA.2023.v25.n1.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a18/

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