Searcharxiv⌕ Search

arXiv subjects

Henrik Rueping

Publications and source records attributed to Henrik Rueping.

9 recordsLinked to original sources
arXiv2022

Multiplicativity and nonrealizable equivariant chain complexes

Let $G$ be a finite $p$-group and $\mathbb{F}$ a field of characteristic $p$. We filter the cochain complex of a free $G$-space with coefficients in $\mathbb{F}$ by powers of the augmentation ideal of $\mathbb{F} G$. We show that the cup product induces a multiplicative structure on the arising spectral sequence and compute the $E_1$-page as a bigraded algebra. As an application, we prove that recent counterexamples of Iyengar and Walker to an algebraic version of Carlsson's conjecture can not be realized topologically.

math.AT↗
arXiv2017

Long and thin covers for flow spaces

Long and thin covers of flow spaces are important ingredients in the proof of the Farrell--Jones conjecture for certain classes of groups, like hyperbolic and CAT(0)-groups. In this paper we provide an alternative construction of such covers which holds in a more general setting and simplifies some of the arguments.

math.AT↗
arXiv2013

Equivariant Refinements

We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of certain covers. Those generalizations play a key role in the proof of the Farrell-Jones conjecture for the general linear group over a finite field.

math.AT↗
arXiv2013

The Farrell-Jones conjecture for S-arithmetic groups

This paper contains the results of my PhD-thesis. I will show the K- and L-theoretic Farrell-Jones conjecture (FJC) for the general linear groups over the rationals and over the rational functions over a finite field. This especially implies the conjecture for all S-arithmetic groups.

math.KT↗