Oscar Ocampo

activity

20232026

most citedCongruence subgroups of braid groups and crystallographic quotients. Part I

1 citations · 1 across the 7 of their papers we have counts for

collaborators

10 papers

math.GR2026

Forbidden relations in universal virtual braid groups

Oscar Ocampo, Charalampos Stylianakis

We study natural automorphisms of the universal virtual braid group $U V_{n} (k)$ . These automorphisms induce commuting involutions in the outer automorphism group and generate a subgr…

math.RT2026

Multi-welded twin groups

Mohamad N. Nasser, Oscar Ocampo

For $k \geq 1$ and $n \geq 2$ , we introduce the multi-welded twin group $M_{k} W T_{n}$ , a natural welded analogue of the multi-virtual twin group. We show that $M_{k} W T_{n}$ arises naturally…

math.RT2026

On Universal Virtual and Welded Braid Groups and Their Linear Representations

Mohamad N. Nasser, Oscar Ocampo

We introduce linear representations of the universal virtual braid group $U V_{n} (c)$ , where $n \geq 2$ and $c \geq 1$ , which is a unifying framework for braid-type groups with multiple…

math.GR2026

Universal virtual braid groups

Oscar Ocampo

We introduce the universal virtual braid group $U V_{n} (c)$ , which provides a unified algebraic framework for virtual braid--type structures with $c$ types of crossings and admits nat…

math.GR2026

Permutational wreath pullbacks and framed braid-type groups

Ênio Leite, Oscar Ocampo

Let $σ : G \to S_{n}$ be a surjective homomorphism and let $H$ be a group. We introduce the \emph{permutational wreath pullback} \[ H \wr_σG = H^n \rtimes_σG, \] where the action…

math.GR2025

Powers of half-twists and congruence subgroups of braid groups

Paolo Bellingeri, Celeste Damiani, Oscar Ocampo +1

In this work, we study the relationship between congruence subgroups $B_{n} [m]$ and $N_{n} (σ_{1}^{m})$ the normal closure of $σ_{1}^{m}$ , where $σ_{1}$ is the classical generator of $B…

math.GT2024

Skew-symmetric augmented matrices and a characterization of virtual doodles

Oscar Ocampo, José Gregorio Rodríguez-Nieto, Olga Patricia Salazar-Díaz

In this paper, we present a brief overview of the concept of doodles from the perspective of J.S. Carter's work on classifying immersed curves and the work of J.S. Carter, S. Kamad…

math.GR2024

Congruence subgroups of braid groups and crystallographic quotients. Part II

Paolo Bellingeri, Celeste Damiani, Oscar Ocampo +1

Following previous work on congruence subgroups and crystallographic braid groups, we study the lower central series of congruence braid groups related to the braid group $B_{3}$ , sh…

math.GR2024★ 1 cited

Congruence subgroups of braid groups and crystallographic quotients. Part I

Paolo Bellingeri, Celeste Damiani, Oscar Ocampo +1

This paper is the first of a two part series devoted to describing relations between congruence and crystallographic braid groups. We recall and introduce some elements belonging t…

math.GR2023

Subgroup separability of surface braid groups and virtual braid groups

Kisnney Almeida, Igor Lima, Oscar Ocampo

In this paper, we study subgroup separability (also known as LERF) and related properties for surface braid groups and virtual (singular) braid groups.