arXiv subjects

Wagner Sgobbi

Publications and source records attributed to Wagner Sgobbi.

3 recordsLinked to original sources

arXiv2026

Property $R_{\infty}$ for groups with infinitely many ends

We show that an accessible group with infinitely many ends has property $R_{\infty}$. That is, it has infinitely many twisted conjugacy classes for any twisting automorphism. We deduce that having property $R_{\infty}$ is undecidable amongst finitely presented groups. We also show that the same is true for a wide class of relatively hyperbolic groups, filling in some of the gaps in the literature. Specifically, we show that a non-elementary, finitely presented relatively hyperbolic group with finitely generated peripheral subgroups which are not themselves relatively hyperbolic, has property $R_{\infty}$.

math.GR↗

arXiv2023

The BNS invariants of the braid groups and pure braid groups of some surfaces

We compute and explicitly describe the Bieri-Neumann-Strebel invariants $Σ^1$ for the full and pure braid groups of the sphere $\mathbb{S}^2$, the real projective plane $\mathbb{R}P^2$ and specially the torus $\mathbb{T}$ and the Klein bottle $\mathbb{K}$. In order to do this for $M=\mathbb T$ or $M=\mathbb K$, and $n \geq 2$, we use the $n^{th}$-configuration space of $M$ to show that the action by homeomorphisms of the group $Out(P_n(M))$ on the character sphere $S(P_n(M))$ contains certain permutation of coordinates, under which $Σ^1(P_n(\mathbb T))^c$ and $Σ^1(P_n(\mathbb K))^c$ are invariant. Furthermore, $Σ^1(P_n(\mathbb T))^c$ and $Σ^1(P_n(\mathbb{S}^2))^c$ (the latter with $n \geq 5$) are finite unions of pairwise disjoint circles, and $Σ^1(P_n(\mathbb K))^c$ is finite. This last fact implies that there is a normal finite index subgroup $H \leq Aut(P_n(\mathbb K))$ such that the Reidemeister number $R(φ)$ is infinite for every $φ\in H$.

math.AT↗

arXiv2022

The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups

We compute the Bieri-Neumann-Strebel invariants $Σ^1$ for the generalized solvable Baumslag-Solitar groups $Γ_n$ and their finite index subgroups. Using $Σ^1$, we show that certain finite index subgroups of $Γ_n$ cannot be isomorphic to $Γ_{k}$ for any $k$. In addition, we use the BNS-invariants to give a new proof of property $R_\infty$ for the groups $Γ_n$ and their finite index subgroups.

math.GR↗