相关论文: Braids act on configurations of lines

We combine the newly discovered technique, which computes explicit formulas for the image of an algebraic curve under rational transformation, with techniques that enable to compute braid monodromies of such curves. We use this combination…

An important piece of information in the theory of the arithmetic Galois action on the geometric fundamental groups of schemes is that divisorial inertia is acted on cyclotomically. We detail in this note the content of this fact in the…

Wiring diagrams usually serve as a tool in the study of arrangements of lines and pseudolines. In this paper we go in the opposite direction, using known properties of line arrangements to motivate certain equivalence relations and actions…

Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, positroid varieties, open Bott-Samelson varieties, and…

Various properties of a class of braid matrices, presented before, are studied considering $N^2 \times N^2 (N=3,4,...)$ vector representations for two subclasses. For $q=1$ the matrices are nontrivial. Triangularity $(\hat R^2 =I)$…

We present a construction of skew monoidal structures from strong actions. We prove that the existence of a certain adjoint allows one to equip the actegory with a skew monoidal structure and that this adjunction becomes monoidal. This…

This article is about Artin's braid group and its role in knot theory. We set ourselves two goals: (i) to provide enough of the essential background so that our review would be accessible to graduate students, and (ii) to focus on those…

In the theory of configuration spaces, "splitting" usually refers to the phenomenon that the configuration spaces on a manifold and those on its punctured version are closely related cohomologically. We prove a splitting theorem that is…

A canonical branched covering over each sufficiently good simplicial complex is constructed. Its structure depends on the combinatorial type of the complex. In this way, each closed orientable 3-manifold arises as a branched covering over…

In the last few years, brane tilings have proven to be an efficient and convenient way of studying supersymmetric gauge theories living on D3-branes or M2-branes. In these pages we present a quick and simple introduction to the subject,…

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups.…

We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not…

This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The…

We introduce and study a family of groups $\mathbf{BB}_n$, called the blocked-braid groups, which are quotients of Artin's braid groups $\mathbf{B}_n$, and have the corresponding symmetric groups $\Sigma_n$ as quotients. They are defined by…

The virtual braid groups are generalizations of the classical braid groups. This paper gives an elementary proof that the classical braid group injects into the virtual braid group over the same number of strands.

We identify natural symmetries of each rigid higher braided category. Specifically, we construct a functorial action by the continuous group $\Omega \mathsf{O}(n)$ on each $\mathcal{E}_{n-1}$-monoidal $(g,d)$-category $\mathcal{R}$ in which…

Braid theory is used to calcualte the topological entropy of data from the belousov-Zhabotinskii reaction, the results agree well with one-dimensional theory to the order of approximation considered.

We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid…

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…

We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…