arXiv subjects

Juliana Roberta Theodoro de Lima

Publications and source records attributed to Juliana Roberta Theodoro de Lima.

3 recordsLinked to original sources

arXiv2026

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

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 many such groups, their explicit structure is often left implicit. In this paper, we give an explicit description of the positive cones defining bi-invariant orderings on almost-direct products of free groups, using normal forms derived from the almost-direct product decomposition together with Magnus-type orderings on free factors. We establish key structural properties of these cones, including compatibility with natural projections, convexity of canonical subgroups, and invariance under suitable classes of automorphisms. As applications, we show how the construction applies to several families of groups of geometric and algebraic interest, such as pure monomial braid groups and McCool groups.

math.GR↗

arXiv2022

An exact sequence for generalized string links over surfaces

In this work we extend Goldberg result \cite{Goldberg} for generalized string links over closed, connected and orientable surfaces of genus $g \geq 1$, i.e., different from the sphere (up to link-homotopy).

math.GT↗

arXiv2019

Homotopy of Braids on Surfaces: extending Goldsmith's Answer to Artin

In 1947, in the paper "Theory of Braids", Artin raised the question of whether isotopy and homotopy of braids on the disk coincide. Twenty seven years later, Goldsmith answered his question: she proved that in fact the group structures are different, exhibiting a group presentation and showing that the homotopy braid group on the disk is a proper quotient of the Artin braid group on the disk $B_{n}$, denoted by $\widehat{B}_{n}$. In this paper, we extend Goldsmith's answer to Artin for closed, connected and orientable surfaces different from the sphere. More specifically, we define the notion of homotopy generalized string links on surfaces, which form a group which is a proper quotient of the braid group on a surface $B_{n}(M)$, denoting it by $\widehat{B}_{n}(M)$. We then give a presentation of the group $\widehat{B}_{n}(M)$ and find that the Goldsmith presentation is a particular case of our main result, when we consider the surface $M$ to be the disk. We close with a brief discussion surrounding the importance of having such a fixed construction available in the literature.

math.AT↗