Oscar Ocampo

activity

20152026

most citedCrystallographic groups and flat manifolds from surface braid groups

4 citations · 17 across the 12 of their papers we have counts for

collaborators

15 papers

hep-th2026

Giant Wilson loops from Fredholm determinants

Ludvig Chen, Victor Mishnyakov, Konstantin Zarembo

We study large-k symmetric and antisymmetric Wilson loops in N=4 super-Yang-Mills theory. We represent their generating functions as Fredholm determinants built from the Hermite ke…

math.GT2025★ 1 cited

The R $_{\infty}$ -property for braid groups over orientable surfaces

Karel Dekimpe, Daciberg Lima Gonçalves, Oscar Ocampo

Let $Σ_{g, p}$ be an orientable surface of genus $g$ and of finite type without boundary (i.e. an orientable closed surface with a finite number $p$ of points removed). In this pape…

math.GR2024

Coxeter-type quotients of surface braid groups

Renato Diniz, Oscar Ocampo, Paulo Cesar Cerqueira dos Santos Júnior

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 clos…

math.GR2024★ 1 cited

Characteristic subgroups and the R $_{\infty}$ -property for virtual braid groups

Karel Dekimpe, Daciberg Lima Gonçalves, Oscar Ocampo

Let $n \geq 2$ . Let $V B_{n}$ (resp. $V P_{n}$ ) denote the virtual braid group (resp. virtual pure braid group), let $W B_{n}$ (resp. $W P_{n}$ ) denote the welded braid group (resp. welded pure…

math.GT2022

Seifert circles, crossing number and the braid index of generalized knots and links

Gustavo Cardoso, Oscar Ocampo

For classical links Ohyama proved an inequality involving the minimal crossing number and the braid index, then motivated from this Takeda showed an analogous inequality for virtua…

math.GR2022

Positive cones and bi-orderings on almost-direct products of free groups

Oscar Ocampo, Juliana Roberta Theodoro de Lima

Almost-direct products of free groups arise naturally in braid theory and in the study of automorphism groups of free groups. Although bi-invariant orderings are known to exist for…

math.GR2022

On virtual singular braid groups

Oscar Ocampo

The virtual singular braid group arises as a natural common generalization of classical singular braid groups and virtual braid groups. In this paper, we study several algebraic pr…

math.GR2021★ 2 cited

Virtual braid groups, virtual twin groups and crystallographic groups

Oscar Ocampo, Paulo Cesar Cerqueira dos Santos Júnior

Let $n \geq 2$ . Let $V B_{n}$ (resp. $V P_{n}$ ) be the virtual braid group (resp. the pure virtual braid group), and let $V T_{n}$ (resp. $P V T_{n}$ ) be the virtual twin group (resp. the pure vi…

math.GR2021★ 1 cited

The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient $B_{n} / [P_{n}, P_{n}]$

Oscar Ocampo, Paulo Cesar Cerqueira dos Santos Júnior

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…

math.GR2021★ 4 cited

Crystallographic groups and flat manifolds from surface braid groups

Daciberg Lima Gonçalves, John Guaschi, Oscar Ocampo +1

Let $M$ be a compact surface without boundary, and $n \geq 2$ . We analyse the quotient group $B_{n} (M) / Γ_{2} (P_{n} (M))$ of the surface braid group $B_{n} (M)$ by the commutator subgroup $Γ…

math.GR2020★ 1 cited

The R $_{\infty}$ property for pure Artin braid groups

Karel Dekimpe, Daciberg Lima Gonçalves, Oscar Ocampo

In this paper we prove that all pure Artin braid groups $P_{n}$ ( $n \geq 3$ ) have the $R_{\infty}$ property. In order to obtain this result, we analyse the naturally induced morphism $\…

math.GT2019★ 3 cited

Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups

Oscar Ocampo

Let $n \geq 3$ . In this paper we show that for any finite abelian subgroup $G$ of $S_{n}$ the crystallographic group $B_{n} / [P_{n}, P_{n}]$ has Bieberbach subgroups $Γ_{G}$ with holonomy gro…

math.GT2018

Almost-crystallographic groups as quotients of Artin braid groups

Daciberg Lima Gonçalves, John Guaschi, Oscar Ocampo

Let $n, k \geq 3$ . In this paper, we analyse the quotient group $B_n /Γ_k (P_n)$ of the Artin braid group $B_n$ by the subgroup $Γ_k (P_n)$ belonging to the lower central series…

math.GT2018★ 1 cited

Embeddings of finite groups in $B_{n} / Γ_{k} (P_{n})$ for $k = 2, 3$

Daciberg Lima Gonçalves, John Guaschi, Oscar Ocampo

Let $n \geq 3$ . In this paper, we study the problem of whether a given finite group $G$ embeds in a quotient of the form $B_{n} / Γ_{k} (P_{n})$ , where $B_{n}$ is the $n$ -string Artin braid g…

math.GR2015★ 3 cited

Quotients of the Artin braid groups and crystallographic groups

Daciberg Lima Gonçalves, John Guaschi, Oscar Ocampo

Let n be greater than or equal to 3. We study the quotient group B\_n/[P n,P\_n] of the Artin braid group B\_n by the commutator subgroup of its pure Artin braid group P\_n. We sho…

Giant Wilson loops from Fredholm determinants

The R∞​-property for braid groups over orientable surfaces

Coxeter-type quotients of surface braid groups

Characteristic subgroups and the R∞​-property for virtual braid groups

Seifert circles, crossing number and the braid index of generalized knots and links

Positive cones and bi-orderings on almost-direct products of free groups

On virtual singular braid groups

Virtual braid groups, virtual twin groups and crystallographic groups

The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient Bn​/[Pn​,Pn​]

Crystallographic groups and flat manifolds from surface braid groups

The R∞​ property for pure Artin braid groups

Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups

Almost-crystallographic groups as quotients of Artin braid groups

Embeddings of finite groups in Bn​/Γk​(Pn​) for k=2,3

Quotients of the Artin braid groups and crystallographic groups

The R $_{\infty}$ -property for braid groups over orientable surfaces

Characteristic subgroups and the R $_{\infty}$ -property for virtual braid groups

The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient $B_{n} / [P_{n}, P_{n}]$

The R $_{\infty}$ property for pure Artin braid groups

Embeddings of finite groups in $B_{n} / Γ_{k} (P_{n})$ for $k = 2, 3$