Konrad Wróbel

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20202026

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math.GR2026

Cost of one-relator groups

Antoine Poulin, Konrad Wróbel

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

math.GR2025

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

Héctor Jardón-Sánchez, Sam Mellick, Antoine Poulin +1

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

math.GR2024

Measurable splittings and the measured group theoretic structure of wreath products

Robin Tucker-Drob, Konrad Wróbel

Let $Γ$ 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 any…

math.GR2024

Infinite volume ends of quotient graphs and homogeneous spaces

Konrad Wróbel

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…