Related papers: On the inverse mapping class monoids

We elaborate on the recent proposal that intersection numbers of certain cohomology classes on the moduli space of genus-zero Riemann surfaces with punctures compute tree-level scattering amplitudes in quantum field theories. The relevant…

Motivated by the work in [15], this paper deals with the theory of the braids from chromatic configuration spaces. This kind of braids possess the property that some strings of each braid may intersect together and can also be untangled, so…

We prove that an Artin-Tits group of type $\tilde C$ is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the "generated group" method. This…

Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or…

We give a complete classification of homomorphisms from the braid group on $n$ strands to the braid group on $2n$ strands when $n$ is at least 5. We also classify endomorphisms of the braid group on 4 strands, as well as homomorphisms from…

We study permutations on n elements preserving orientation (parity) of every subset of size k. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral.…

We construct a new monoid structure for Artin groups associated with finite Coxeter systems. This monoid shares with the classical positive braid monoid a crucial algebraic property: it is a Garside monoid. The analogy with the classical…

This thesis studies skein relations in cluster algebras arising from punctured surfaces. We introduce skein-type identities expressing cluster variables associated with incompatible curves on a surface in terms of cluster variables…

We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is…

A generalization of the topological fundamental group is developed in order to exhibit a topologically complete braid group containing Artin's braid group on infinitely many strands with respect to the following notion of convergence: A…

We associate to every positive braid a braid monodromy group, generalizing the geometric monodromy group of an isolated plane curve singularity. If the closure of the braid is a knot, we identify the corresponding group with a framed…

Let $\Gamma$ be a finite connected graph. The (unlabelled) configuration space $UC^n \Gamma$ of $n$ points on $\Gamma$ is the space of $n$-element subsets of $\Gamma$. The $n$-strand braid group of $\Gamma$, denoted $B_n\Gamma$, is the…

Let $S$ and $X$ be two connected topological surfaces without boundary, and assume that $S$ is either of infinite type or has negative Euler characteristic. In this paper, we prove that if $p:S\rightarrow X$ is a fully ramified branched…

We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence within this class of groups in terms of the defining graph.…

We generalize a discovery of Kasahara and show that the Jones representations of braid groups, when evaluated at $q = -1$, are related to the action on homology of a branched double cover of the underlying punctured disk. As an application,…

In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad…

In this paper we define a new family of groups which generalize the {\it classical braid groups on} $\C $. We denote this family by $\{B_n^m\}_{n \ge m+1}$ where $n,m \in \N$. The family $\{ B_n^1 \}_{n \in \N}$ is the set of classical…

Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer's faithfulness proof for this linear representation to Artin groups of finite type.

Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n $\in$ N for which there exists a surjection between the n-and m-string braid groups of an orientable surface without boundary. This…

Let M be a compact, connected surface, possibly with a finite set of points removed from its interior. Let d,n be positive integers, and let N be a d-fold covering space of M. We show that the covering map induces an embedding of the n-th…