相关论文: Solution of the quasipositivity problem in the bra…

Let $A$ be a Hopf algebra in a braided category $\cal C$. Crossed modules over $A$ are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category $\DY{\cal C}^A_A$ of…

We show that the problem of constructing a real rational knot of a reasonably low degree can be reduced to an algebraic problem involving the pure braid group: expressing an associated element of the pure braid group in terms of the…

We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the $K(\pi,1)$ conjecture holds for the associated family of Artin groups this establishes homological stability…

We prove that a commutative parasemifield S is additively idempotent provided that it is finitely generated as a semiring. Consequently, every proper commutative semifield T that is finitely generated as a semiring is either additively…

The aim of the present note is to construct invariants of the Artin braid group valued in $G_{N}^{2}$, and further study of groups related to $G_{n}^{3}$. In the groups $G_{n}^{2}$, the word problem is solved; these groups are much simpler…

In this short note we provide an alternative proof of a theorem of Kapovich and Millson about the Malcev completion of an arbitrary Artin group, and determine the Malcev completion of the braid group of an irreducible finite complex…

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin-Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the…

We give a solution to the word problem for the singular braid monoid SB_n. The complexity of the algorithm is quadratic in the product of the word length and the number of the singular generators in the word. Furthermore we algebraically…

Quasi-rigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasi-rigidity a complete theory for these granular assemblies?…

We describe the most efficient solutions to the word problem of Artin's braid group known so far, i.e., in other words, the most efficient solutions to the braid isotopy problem, including the Dynnikov method, which could be especially…

The notions of stable and Morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word-hyperbolic group. For a word-hyperbolic group $G$, Kapovich provided a partial algorithm which, on input a…

In the first part we review some topological and algebraic aspects in the theory of Artin and Coxeter groups, both in the finite and infinite case (but still, finitely generated). In the following parts, among other things, we compute the…

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 that finite index subgroups of right angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups. In particular, we show that any word hyperbolic Coxeter group…

We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups…

We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the…

We classify the groups quasi-isometric to a group generated by finite-order elements within the class of one-ended hyperbolic groups which are not Fuchsian and whose JSJ decomposition over two-ended subgroups does not contain rigid vertex…

Consider an element~$x$ of a Garside group which is rigid in the sense of Garside-theory. Let $SC(x)$ be the set of rigid conjugates of~$x$ -- this is a well-known characteristic subset of the conjugacy class of~$x$. We present…

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 give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic $13$-space, take the quotient of the remaining space by a discrete group, and find generators for the…