Related papers: Smallest non-cyclic quotients of braid and mapping…

We improve the existing lower bounds on the order of counterexamples to a conjecture by P. Schmid, determine some properties of the possible counterexamples of minimum order for each prime, and the isomorphism type of the center of the…

In this paper, we will develop a family of braid representations of Artin groups of type B from braided vector spaces, and identify the homology of these groups with these coefficients with the cohomology of a specific bimodule over a…

In 2017, Qiao and Koolen showed that for any fixed integer $D\geq 3$, there are only finitely many such graphs with $\theta_{\min}\leq -\alpha k$, where $0<\alpha<1$ is any fixed number. In this paper, we will study non-bipartite…

In this paper we introduce a class of `parabolic' subgroups for the generalized braid group associated to an arbitrary irreducible complex reflection group, which maps onto the collection of parabolic subgroups of the reflection group.…

Denote the alternating and symmetric groups of degree $n$ by $A_n$ and $S_n$ respectively. Consider a permutation $\sigma\in S_n$ all of whose nontrivial cycles are of the same length. We find the minimal polynomials of $\sigma$ in the…

We present an algorithm that computes a shortest non-contractible and a shortest non-separating cycle on an orientable combinatorial surface of bounded genus in O(n \log n) time, where n denotes the complexity of the surface. This solves a…

We give a new proof of the absence of non-trivial idempotents in the group ring of torsion-free cocompact lattices in SL(n,C). It is based on the following procedure. We lift the class of the trace in the cyclic cohomology of the group ring…

Let $G$ be an unicyclic graph of order $n$ and let $Q_G(x)= det(xI-Q(G))={matrix} \sum_{i=1}^n (-1)^i \varphi_i x^{n-i}{matrix}$ be the characteristic polynomial of the signless Laplacian matrix of a graph $G$. We give some transformations…

The (n,k)-arrangement graph A(n,k) is a graph with all the k-permutations of an n-element set as vertices where two k-permutations are adjacent if they agree in exactly k-1 positions. We introduce a cyclic decomposition for k-permutations…

Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus $g$ with one boundary component, that are double coverings of…

This paper describes some generalizations of the results presented in the book "Geometry of defining Relations in Groups" , of A.Yu.Ol'shanskii to the case of non-cyclic torsion-free hyperbolic groups. In particular, it is proved that for…

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…

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification…

There has been interest recently concerning when a left ordered group is locally indicable. Bergman and Tararin have shown that not all left ordered groups are locally indicable, but all known examples contain a nonabelian free subgroup. We…

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…

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every…

Let A_r be the minimal resolution of the cyclic quotient singularity C^2/Z_{r+1}. We study the equivariant quantum cohomology ring of the n-fold symmetric product stack [Sym^n(A_r)] of A_r. We calculate the operators of quantum…

We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols algebra in the Yetter-Drinfeld category over W. This gives a…

In 1869, Jordan proved that the set $\mathcal{T}$ of all finite group that can be represented as the automorphism group of a tree is containing the trivial group and it is closed under taken direct product of groups of lower order in…

Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes…