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Commutative algebra for cohomology rings of classifying spaces of compact Lie groups

โœ Scribed by D.J. Benson; J.P.C. Greenlees

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
827 KB
Volume
122
Category
Article
ISSN
0022-4049

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โœฆ Synopsis

We apply the techniques of highly structured ring and module spectra to prove a duality theorem for the cohomology ring of the classifying space of a compact Lie group. This generalizes results of 31 and Greenlees [lo] in the case of finite groups. In particular, we prove a functional equation for the Poincare series in the oriented Cohen-Macaulay case.

๐Ÿ“œ SIMILAR VOLUMES

Commutative Algebra for Cohomology Rings
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โœ D.J. Benson; J.P.C. Greenlees ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 285 KB

Cohomology rings of finite groups have strong duality properties, as shown by w x w x Benson and Carlson 4 and Greenlees 16 . We prove here that cohomology rings of virtual duality groups have a ring theoretic duality property, which combines the duality properties of finite groups with the cohomolo

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We compute the center and nilpotency of the graded Lie algebra \* ( Baut1(X ))โŠ—Q for a large class of formal spaces X: The latter calculation determines the rational homotopical nilpotency of the space of self-equivalences aut1(X ) for these X . Our results apply, in particular, when X is a complex