Related papers: Questions on surface braid groups

In this paper we give new presentations of the braid groups and the pure braid groups of a closed surface. We also give an algorithm to solve the word problem in these groups, using the given presentations.

We give presentations of braid groups and pure braid groups on surfaces.

A large class of positive finite presentations of the braid groups is found and studied. It is shown that no presentations but known exceptions in this class have the property that equivalent braid words are also equivalent under positive…

The conjugacy problem in braid groups has been extensively studied, particularly from an algorithmic perspective. Established methods based on Garside structures, such as initial summit sets and super summit sets, provide effective…

We study a subset of square free positive braids and we give a few algebraic characterizations of them and one geometric characterization: the set of positive braids whose closures are unlinks. We describe canonical forms of these braids…

A new presentation of the $n$-string braid group $B_n$ is studied. Using it, a new solution to the word problem in $B_n$ is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes…

We give presentations, in terms of generators and relations, for the monoids of singular braids on closed surfaces. The proof of the validity of these presentations can also be applied to verify, in a new way, the presentations given by…

In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study…

In the paper we give a survey on braid groups and subjects connected with them. We start with the initial definition, then we give several interpretations as well as several presentations of these groups. Burau presentation for the pure…

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands,…

We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.

Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…

We provide a characterization for multitwists satisfying the braid relation in the mapping class group of an orientable surface.

We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…

For an oriented surface link $S$, we can take a satellite construction called a 2-dimensional braid over $S$, which is a surface link in the form of a covering over $S$. We demonstrate that 2-dimensional braids over surface links are useful…

This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.

We determine the lower central series and corresponding residual properties for braid groups and pure braid groups of orientable surfaces.

Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid…

We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include…

In this paper we study abelian and metabelian quotients of braid groups on oriented surfaces with boundary components. We provide group presentations and we prove rigidity results for these quotients arising from exact sequences related to…