Results 51 to 60 of about 5,399,954 (113)
CAT(0) and cubulated Shephard groups
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well‐known result that Coxeter groups are CAT(0)$\mathrm{CAT}(0)$ to a class of Shephard ...
Katherine M. Goldman
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Dynamical cocycles with values in the Artin braid group [PDF]
Ergodic Theory and Dynamical Systems, 1999 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 properties of this cocycle and derive a series of topological invariants for the diffeomorphism which enjoy rich ...
Gambaudo, J.-M., Pécou, E. E.
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PBW Deformations of Smash Products Involving Hopf Algebra of Kac–Paljutkin Type
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let H2n2 be the Kac–Paljutkin–type Hopf algebra of dimension 2n2, A its graded Koszul Artin–Schelter regular H2n2‐module algebra of Dimension 2, A! the Koszul dual of A, and Acop the braided‐opposite algebra of A. This paper describes (0, 1)‐degree PBW deformations of the smash product A♯H2n2 and those of A!♯H2n2 under the condition that the Koszul ...
Yujie Gao, Shilin Yang, Naihuan Jing
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Link splitting deformation of colored Khovanov–Rozansky homology
Proceedings of the London Mathematical Society, Volume 129, Issue 3, September 2024.Abstract We introduce a multiparameter deformation of the triply‐graded Khovanov–Rozansky homology of links colored by one‐column Young diagrams, generalizing the “y$y$‐ified” link homology of Gorsky–Hogancamp and work of Cautis–Lauda–Sussan. For each link component, the natural set of deformation parameters corresponds to interpolation coordinates on ...
Matthew Hogancamp +2 more
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Tits alternatives for graph products
, 2015 We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group satisfies this ...
Antolin, Yago, Minasyan, Ashot
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Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.Abstract Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$, the m$m$‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$. The classical Shi arrangement (m=0$m=0$) was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for W$W$.
Matthew Dyer +3 more
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Braid groups, Artin groups and their applications in cryptography
, 2003 The aim of this article is to show how the braid groups can serve as a good platform to enrich cryptography. Braid groups are useful to cryptography for a number of reasons: (i) the word problem is solved via a fast algorithm which computes the canonical
Webster, Catherine
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COMPLETING ARTIN'S BRAID GROUP ON INFINITELY MANY STRANDS [PDF]
Journal of Knot Theory and Its Ramifications, 2005 A generalization of the topological fundamental group is developed in order to construct a completion of Artin's braid group on infinitely many strands with respect to the following notion of convergence: bn → id iff for each M > 0, eventually the first M strands of bn are trivial.
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Rational cross‐sections, bounded generation, and orders on groups
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We provide new examples of groups without rational cross‐sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Our examples contain a finitely presented HNN‐extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word
Corentin Bodart
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The generalized Harer conjecture for the homology triviality
Bulletin of the London Mathematical Society, Volume 56, Issue 5, Page 1879-1895, May 2024.Abstract The classical Harer conjecture states the stable homology triviality of the canonical embedding ϕ:B2g+2↪Γg$\phi: B_{2g+2} \hookrightarrow \Gamma _{g}$, which was proved by Song and Tillmann. The main part of the proof is to show that Bϕ+:BB∞+→BΓ∞+$\operatorname{B}\phi ^{+}: \operatorname{B}B_{\infty }^{+} \rightarrow \operatorname{B}\Gamma _ ...
Wonjun Chang +2 more
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