A. Jaikin‐Zapirain

activity

20032026

most citedFree factors and profinite completions

3 citations · 4 across the 16 of their papers we have counts for

collaborators

Showing math.GRShow all

18 papers · 1 filter

math.GR2026

Average Numbers of Homomorphisms to Random Modules over Free Group Algebras

J. de la Nuez González, Andrei Jaikin-Zapirain

Let $F$ be a finitely generated free group, and let $L$ be a finitely presented $F_{q} [F]$ -module. We study the average number $Λ_{L} (n)$ of $F_{q} [F]$ -module homomorph…

math.GR2026

Thurston norm, polytopes and splitting complexity

Andrei Jaikin-Zapirain, Monika Kudlinska, Pablo Sánchez-Peralta

Let $G$ be a finitely generated torsion-free group satisfying the Strong Atiyah Conjecture. Assuming that $b_{1}^{(2)} (G) = 0$ , we associate to each surjective integral character $ϕ$ t…

math.GR2025

Group pairs, coherence and Farrell--Jones Conjecture for $K_{0}$

Andrei Jaikin-Zapirain, Marco Linton, Pablo Sánchez-Peralta

A group pair $(G, X)$ consists of a group $G$ together with a $G$ -set $X$ . Such a pair encodes properties of $G$ relative to the stabilisers of points in $X$ . In this paper, we sho…

math.GR2024

Free groups are $L^{2}$ -subgroup rigid

Andrei Jaikin-Zapirain

In this paper, we introduce the notion of $L^{2}$ -subgroup rigid groups and demonstrate that free groups are $L^{2}$ -subgroup rigid. As a consequence, we establish the equivalence betw…

math.GR2024

Sylvester domains and pro- $p$ groups

Andrei Jaikin-Zapirain, Henrique Souza

Let $G$ be a finitely generated torsion-free pro- $p$ group containing an open free-by- $Z_{p}$ pro- $p$ subgroup. We show that the completed group algebra of $G$ over $\mathbb…

math.GR2024

Some remarks on Grothendieck pairs

Andrei Jaikin-Zapirain, Alexander Lubotzky

We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We al…

Average Numbers of Homomorphisms to Random Modules over Free Group Algebras

Thurston norm, polytopes and splitting complexity

Group pairs, coherence and Farrell--Jones Conjecture for K0​

Free groups are L2-subgroup rigid

Sylvester domains and pro-p groups

Some remarks on Grothendieck pairs

Group pairs, coherence and Farrell--Jones Conjecture for $K_{0}$

Free groups are $L^{2}$ -subgroup rigid

Sylvester domains and pro- $p$ groups