The Steenrod problem of realizing polynomial cohomology rings

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dc.creatorAndersen, Kasper K. S.
dc.creatorGrodal, Jesper
dc.date2007-04-30
dc.date2008-08-04
dc.date.accessioned2026-07-07T12:22:15Z
dc.date.available2026-07-07T12:22:15Z
dc.descriptionIn this paper we completely classify which graded polynomial R-algebras in finitely many even degree variables can occur as the singular cohomology of a space with coefficients in R, a 1960 question of N. E. Steenrod, for a commutative ring R satisfying mild conditions. In the fundamental case R = Z, our result states that the only polynomial cohomology rings over Z which can occur, are tensor products of copies of H^*(CP^\infty;Z) = Z[x_2], H^*(BSU(n);Z) = Z[x_4,x_6,...,x_{2n}], and H^*(BSp(n):Z) = Z[x_4,x_8,...,x_{4n}] confirming an old conjecture. Our classification extends Notbohm's solution for R = F_p, p odd. Odd degree generators, excluded above, only occur if R is an F_2-algebra and in that case the recent classification of 2-compact groups by the authors can be used instead of the present paper. Our proofs are short and rely on the general theory of p-compact groups, but not on classification results for these.
dc.description14 pages. v3: Final version. To appear in Journal of Topology
dc.identifierhttps://arxiv.org/abs/0704.4002
dc.identifierhttp://arxiv.org/abs/0704.4002
dc.identifierJ Topology 2008 1: 747-760
dc.identifierdoi:10.1112/jtopol/jtn021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213591
dc.subjectAlgebraic Topology
dc.subjectGroup Theory
dc.subject55N10; 55R35, 55R40
dc.titleThe Steenrod problem of realizing polynomial cohomology rings
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