arXiv subjects

Paulo Cesar Cerqueira dos Santos Júnior

Publications and source records attributed to Paulo Cesar Cerqueira dos Santos Júnior.

3 recordsLinked to original sources

arXiv2024

Coxeter-type quotients of surface braid groups

Let $M$ be a closed surface, $q\geq 2$ and $n\geq 2$. In this paper, we analyze the Coxeter-type quotient group $B_n(M)(q)$ of the surface braid group $B_{n}(M)$ by the normal closure of the element $σ_1^q$, where $σ_1$ is the classic Artin generator of the Artin braid group $B_n$. Also, we study the Coxeter-type quotient groups obtained by taking the quotient of $B_n(M)$ by the commutator subgroup of the respective pure braid group $[P_n(M),P_n(M)]$ and adding the relation $σ_1^q=1$, when $M$ is a closed orientable surface or the disk.

math.GR↗

arXiv2023

Virtual braid groups, virtual twin groups and crystallographic groups

Let $n\ge 2$. Let $VB_n$ (resp. $VP_n$) be the virtual braid group (resp. the pure virtual braid group), and let $VT_n$ (resp. $PVT_n$) be the virtual twin group (resp. the pure virtual twin group). Let $Π$ be one of the following quotients: $VB_n/Γ_2(VP_n)$ or $VT_n/Γ_2(PVT_n)$ where $Γ_2(H)$ is the commutator subgroup of $H$. In this paper, we show that $Π$ is a crystallographic group and we characterize the elements of finite order and the conjugacy classes of elements in $Π$. Furthermore, we realize explicitly some Bieberbach groups and infinite virtually cyclic groups in $Π$. Finally, we also study other braid-like groups (welded, unrestricted, flat virtual, flat welded and Gauss virtual braid group) module the respective commutator subgroup in each case.

math.GR↗

arXiv2021

The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient $B_n/[P_n,P_n]$

Let $n\geq 3$. In this paper we deal with the conjugacy problem in the Artin braid group quotient $B_n/[P_n,P_n]$. To solve it we use systems of equations over the integers arising from the action of $B_n/[P_n,P_n]$ over the abelianization of the pure Artin braid group $P_n/[P_n,P_n]$. Using this technique we also realize explicitly infinite virtually cyclic subgroups in $B_n/[P_n,P_n]$.

math.GR↗