Local cohomology in equivariant topology (Q2776423)

This article is a quite complete survey on the mathematical work of the author on several topics for which the interaction between topology and commutative algebra are relevant. The paper focusses mainly on the understanding of the equivariant cohomology and homology of universal spaces. The author shows how to use a combination of the local cohomology theorems together with the universal coefficient theorem to obtain some interesting duality statements related to Gorenstein conditions. Along his work, he provides the reader with enlightening examples mainly devoted to cyclic groups, \(p\)-groups and particularly the case \( G=C_{2}\). This paper becomes a useful reference tool for those interested in both topology and commutative algebra. The final third contains an illuminating proof of the existence of a spectral sequence connecting equivariant cobordism and local cohomology, valid for \(G\)-spaces with \(G\) a finite group.NEWLINENEWLINEFor the entire collection see [Zbl 0974.00036].