arXiv subjects

Henrik Rüping

Publications and source records attributed to Henrik Rüping.

4 recordsLinked to original sources

arXiv2025

Steenrod closed $C_3$-invariant parameter ideals in the mod 2 cohomology of $\mathbb{Z}/2\times\mathbb{Z}/2$

For the nontrivial action by the cyclic group $C_3$ of order $3$ on the graded polynomial ring $\mathbb{F}_2[a,b]$, we classify the $C_3$-invariant parameter ideals that are closed under Steenrod operations. The classification has applications to free actions by the Klein four-group $\mathbb{Z}/2\times\mathbb{Z}/2$ on products of two spheres (and more generally, finite CW complexes with four-dimensional mod $2$ homology) that extend to actions by the alternating group $A_4=(\mathbb{Z}/2\times\mathbb{Z}/2)\rtimes C_3$.

math.AT↗

arXiv2025

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

In this paper, we classify the parameter ideals in $H^*(BA_4;\mathbb{F}_2)$ and in the Dickson algebra $H^*(BSO(3);\mathbb{F}_2)$ that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions $n,m$ for which $A_4$ (and $SO(3)$) can act freely on $S^n\times S^m$.

math.AT↗

arXiv2024

An equivariant BGG correspondence and perfect complexes for extensions by $\mathbb{Z}/2\times \mathbb{Z}/2$

We provide an equivariant extension of Carlsson's BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of $(\mathbb{Z}/2\times \mathbb{Z}/2)\rtimes Q$-representations with four-dimensional total homology for finite groups $Q$ of odd order. We deduce that cochain complexes of finite, free $A_4$-CW complexes with four-dimensional total homology are rigid: They are determined by the degrees of the nonzero homology groups.

math.AC↗

arXiv2022

Automorphisms of the Koszul homology of a local ring

This work concerns the Koszul complex $K$ of a commutative noetherian local ring $R$, with its natural structure as differential graded $R$-algebra. It is proved that under diverse conditions, involving the multiplicative structure of $H(K)$, any dg $R$-algebra automorphism of $K$ induces the identity map on $H(K)$. In such cases, it is possible to define an action of the automorphism group of $R$ on $H(K)$. On the other hand, numerous rings are described for which $K$ has automorphisms that do not induce the identity on $H(K)$. For any $R$, it is shown that the group of automorphisms of $H(K)$ induced by automorphisms of $K$ is abelian.

math.AC↗