Related papers: Artin braid groups and spin structures

The object of this paper is to study GL(2,R) orbit closures in hyperelliptic components of strata of abelian differentials. The main result is that all higher rank affine invariant submanifolds in hyperelliptic components are branched…

By considering the way an n-tuple of points in the 2-disk are linked together under iteration of an orientation preserving diffeomorphism, we construct a dynamical cocycle with values in the Artin braid group. We study the asymptotic…

We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is…

Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.…

In this paper we compute the automorphism groups $\operatorname{Aut}(\mathbf{P}_n(\Sigma))$ and $\operatorname{Aut}(\mathbf{B}_n(\Sigma))$ of braid groups $\mathbf{P}_n(\Sigma)$ and $\mathbf{B}_n(\Sigma)$ on every orientable surface…

This thesis takes Brady's construction of $K(\pi,1)$s for the braid groups as a starting point. It is widely known that this construction can - with the right ingredients - be generalized to Artin groups of finite type. Results of Bessis as…

We examine the construction of Huang and Osajda that was used in their proof of the biautomaticity of Artin groups of almost large type. We describe a slightly simpler variant of that biautomatic structure, with explicit descriptions of a…

We develop a theory of Brill-Noether divisors on the moduli space of stable spin curves of genus g, and compute the classes of these loci. A spin Brill-Noether cycle is defined in terms of the relative position of the spin structure with…

We observe that, for each positive integer n > 2, each of the Artin groups of finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is a central extension of a finite index subgroup of the mapping class group of the…

We show that each of the Artin groups of type $B_n$ and $D_n$ can be presented as a semidirect product $F \rtimes {\cal B}_n$, where $F$ is a free group and ${\cal B}_n$ is the $n$-string braid group. We explain how these semidirect product…

We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy…

Herein we prove that if $M$ is a compact oriented Riemann surface of genus $g$, and $M^{[n]}$ is the classifying space of $n$ distinct, unordered points on $M$, then the kernel of the map $\pi_1(M^{[n]})\to H_1(M)$ is generated by…

We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled…

In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in…

Moduli spaces of points on $n$-spheres carry natural actions of braid groups. For $n=0$, $1$, and $3$, we prove that these symmetries extend to actions of mapping class groups of positive genus surfaces, by establishing exceptional…

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular,…

We determine a classification of the endomorphisms of the Artin groups of spherical type $B_n$ for $n\ge 5$, and of their quotients by the center.

Let S be a closed oriented surface of genus g > 1, and let T denote its Torelli group. First, given a set E of homotopically nontrivial, pairwise disjoint, pairwise nonisotopic simple closed curves on S, we determine precisely when a…

We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K_2. We also verify the Beilinson conjectures about K_2 numerically for several curves with g=2, 3, 4 and 5. The paper is…

Let $\Sigma_g$ denote the closed orientable surface of genus $g$ and fix an arbitrary simplicial triangulation of $\Sigma_g$. We construct and study a natural surjective group homomorphism from the surface braid group on $n$ strands on…