| Title | The Steenrod problem of realizing polynomial cohomology rings |
| Authors | Kasper Andersen, Jesper Grodal |
| Alternative Location | http://jtopol.oxfordjournal..., Restricted Access |
| Alternative Location | http://dx.doi.org/10.1112/j..., Restricted Access |
| Publication | Journal of Topology |
| Year | 2008 |
| Volume | 1 |
| Issue | 4 |
| Pages | 747 - 760 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Oxford UP / London Mathematical Society |
| Abstract English | In this paper, we completely classify which graded polynomial<br> 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 that can occur are tensor products of copies of $H^*(CP^\infty;Z)\cong Zx_2$,<br> $H^*(BSU(n);Z)\cong Zx_4, x_6, \ldots, x_{2n}$, and<br> $H^*(BSp(n);Z)\cong Zx_4, x_8, \ldots, x_{4n}$, 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<br> 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<br> p-compact groups, but not on classification results for these. |
| ISBN/ISSN/Other | ISSN: 1753-8424 (online) |
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