Konrad Wróbel

activity

20242026

collaborators

4 papers

math.GR2026

Cost of one-relator groups

Antoine Poulin, Konrad WrÃ³bel

For any infinite one-relator group $I^ = ⟨ S ∣ w^{m} ⟩$ , we prove that $cost (I^) = ∣ S ∣ - \frac{1}{m}$ . For such groups, this gives $Î²^{(2)}_1(Î)=\mathrm{cost}(Î)…

math.GR2026

Exactness and the topology of the space of invariant random equivalence relations

HÃ©ctor JardÃ³n-SÃ¡nchez, Sam Mellick, Antoine Poulin +1

We characterize exactness of a countable group $I^$ in terms of invariant random equivalence relations (IREs) on $I^$ . Specifically, we show that $I^$ is exact if and only if every…

math.GR2025

Infinite volume ends of quotient graphs and homogeneous spaces

Konrad WrÃ³bel

We introduce the space of infinite volume ends of a locally compact second countable (lcsc) space that admits a Radon measure. In certain cases, this coincides with the classical s…

math.GR2024

Measurable splittings and the measured group theoretic structure of wreath products

Robin Tucker-Drob, Konrad WrÃ³bel

Let $I^$ be a countable group that admits an essential measurable splitting (for instance, any group measure equivalent to a free product of nontrivial groups). We show: (1) for an…