Related papers: From braid groups to mapping class groups
Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we…
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…
We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts. In this article we tie recent work on various other natural overgroups, in…
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a…
In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.
The paper deals with braided Clifford algebras, understood as Chevalley-Kahler deformations of braided exterior algebras. It is shown that Clifford algebras based on involutive braids can be naturally endowed with a braided quantum group…
We compare two crossed homomorphisms on a braid group, one defined diagrammatically and the other defined algebraically. We show that these crossed homomorphisms are essentially the same, and compute them in detail for simple braids, namely…
We survey stability properties of several families of moduli spaces, with a focus on braid groups and configuration spaces.
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
This paper will appear in the Santa Cruz proceedings. An overview of the braid group techniques in the theory of algebraic surfaces, from Zariski to the latest results, is presented. An outline of the Van Kampen algorithm for computing…
This is an introduction to the braid groups, as presented in the summer school and workshop on braid groups at the National University of Singapore in June 2007.
We associate each endomorphism of a finite cyclic group with a digraph and study many properties of this digraph, including its adjacent matrix and automorphism group.
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
A construction of braid group actions on coherent sheaves using mixed Hodge modules and some well known constructions from geometric representation theory is given.
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
We study the action of (big) mapping class groups on the first homology of the corresponding surface. We give a precise characterization of the image of the induced homology representation.
The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal M$, as the disjoint union of the braid groups $\mathcal B$ does. We give a concrete, and geometric meaning of the braiding $\beta_{r,s}$ in…
In this note we prove that the mapping class group of a compact topological manifold $M$ with boundary is of finite type, under assumptions on its dimension and connectivity.