Steenrod closed parameter ideals in the mod-$2$ cohomology of $A_4$ and $SO(3)$

Henrik Rüping; Marc Stephan; Ergun Yalcin

paper

Steenrod closed parameter ideals in the mod- $2$ cohomology of $A_{4}$ and $S O (3)$

arXiv:2206.11802

Abstract

In this paper, we classify the parameter ideals in $H^{*} (B A_{4}; F_{2})$ and in the Dickson algebra $H^{*} (B S O (3); F_{2})$ that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions $n, m$ for which $A_{4}$ (and $S O (3)$ ) can act freely on $S^{n} \times S^{m}$ .

37 pages, 1 figure; v2: removed sections 8 and 9 to shorten the paper, added Theorem 1.4; v3: minor changes, final version

Steenrod closed parameter ideals in the mod-2 cohomology of A4​ and SO(3)

Abstract

Steenrod closed parameter ideals in the mod- $2$ cohomology of $A_{4}$ and $S O (3)$