A. Jaikin‐Zapirain

activity

20032026

(T)

for noncommutative universal lattices

40 citations · 87 across the 23 of their papers we have counts for

collaborators

26 papers

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