Related papers: Brunnian Braids on Surfaces

On the basis of recent results on hamiltonicity and hamiltonian connectedness in the square of a 2-block, we determine the most general block-cutvertex structure a graph $G$ may have in order to guarantee that $G^2$ is hamiltonian,…

In this note we provide explicit generators of the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular, for all Brauer-Severi surfaces. To produce these generators we use the Twisting Theory for smooth…

We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings are shepherded. We consider the problem as Hamiltonian {\it scattering} of a large number of non-interacting massless…

In this paper we compute the homotopy groups of the symplectomorphism groups of the 3-, 4- and 5-point blow-ups of the projective plane (considered as monotone symplectic Del Pezzo surfaces). Along the way, we need to compute the homotopy…

We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of…

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 $\sigma_1^q$, where $\sigma_1$ is the…

In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of…

We describe all groups that can be generated by two twists along spherical sequences in an enhanced triangulated category. It will be shown that with one exception such a group is isomorphic to an abelian group generated by not more than…

In this paper, we classify homomorphisms from the braid group of $n$ strands to the mapping class group of a genus $g$ surface. In particular, we show that when $g<n-2$, all representations are either cyclic or standard. Our result is sharp…

In this paper we generate and systematically classify all prime planar knotoids with up to 5 crossings. We also extend the existing list of knotoids in $S^2$ and add all knotoids with 6 crossings.

We consider subgroups of the braid groups which are generated by $k$-th powers of the standard generators and prove that any infinite intersection (with even $k$) is trivial. This is motivated by some conjectures of Squier concerning the…

We introduce an algorithmic framework to investigate spherical and geodesic growth series of braid groups relatively to the Artin's or Birman-Ko-Lee's generators. We present our experimentations in the case of three and four strands and…

We study a novel type of braid groups on a closed orientable surface $\Sigma$. These are fundamental groups of certain manifolds that are hybrids between symmetric products and configuration spaces of points on $\Sigma$; a class of examples…

We completely determine finite abelian regular branched covers of the 2-sphere $S^2$ with the property that each homeomorphism of $S^2$ preserving the branching set can be lifted.

The paper is devoted to the study of exact curves on Arborealized Liouville surfaces. We introduce the notion of a generating family for such curves. Our main statement is a hamiltonian lifting property: the set of curves admitting a…

We consider an area-preserving diffeomorphism of a compact surface, which is assumed to be an irrational rotation near each boundary component. A finite set of periodic orbits of the diffeomorphism gives rise to a braid in the mapping…

We consider braids on $m+n$ strands, such that the first $m$ strands are trivially fixed. We denote the set of all such braids by $B_{m,n}$. Via concatenation $B_{m,n}$ acquires a group structure. The objective of this paper is to find a…

We prove that generic elements of braid groups are pseudo-Anosov, in the following sense: in the Cayley graph of the braid group with n $\ge$ 3 strands, with respect to Garside's generating set, we prove that the proportion of pseudo-Anosov…

We prove a division algorithm for group rings of high genus surface groups and use it to show that some $2$-complexes with surface fundamental groups are standard. We also give an application of division to cohomological dimension of…

We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.