Pablo S'anchez-Peralta

activity

20232026

collaborators

6 papers

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.GR2026

Coherent RFRS groups

Sam P. Fisher, Marco Linton, Pablo Sánchez-Peralta

We prove that a finitely generated virtually RFRS group of cohomological dimension at most $2$ is coherent if and only if its second $L^{2}$ -Betti number vanishes if and only if it…

math.GT2026

Simon's knot genus problem and Lewin $3$ -manifold groups

Pablo Sánchez-Peralta

We provide a positive answer to an old problem of Jonathan K. Simon: if $K$ and $K^{'}$ are two knots such that there is an epimorphism from the knot group of $K$ to the knot group of…

math.GR2026

On the top-dimensional $L^{2}$ -Betti number of residually poly- $Z$ groups

Sam P. Fisher, Pablo Sánchez-Peralta

Let $G$ be a residually poly- $Z$ group of finite type. We prove that $G$ admits a poly- $Z$ quotient with kernel $N$ satisfying $\mathrm{cd}_{\mathbb Q}(N) < \mathbb…

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.GR2023

On vanishing criteria of $L^{2}$ -Betti numbers of groups

Pablo Sánchez-Peralta

Let $G$ be a countable group and $k$ a positive integer, we show that the $L^{2}$ -Betti numbers of the group $G$ vanish up to degree $k$ provided that there is some infinite index su…

Thurston norm, polytopes and splitting complexity

Coherent RFRS groups

Simon's knot genus problem and Lewin 3-manifold groups

On the top-dimensional L2-Betti number of residually poly-Z groups

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

On vanishing criteria of L2-Betti numbers of groups

Simon's knot genus problem and Lewin $3$ -manifold groups

On the top-dimensional $L^{2}$ -Betti number of residually poly- $Z$ groups

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

On vanishing criteria of $L^{2}$ -Betti numbers of groups