Results 31 to 40 of about 321 (123)
Homogeneous braids are visually prime
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primeness of open books, which we consider to be of independent interest.
Peter Feller +2 more
wiley +1 more source
The Dehn twist coefficient for big and small mapping class groups
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract We study a quasimorphism, which we call the Dehn twist coefficient (DTC), from the mapping class group of a surface (with a chosen compact boundary component) that generalizes the well‐studied fractional Dehn twist coefficient (FDTC) to surfaces of infinite type. Indeed, for surfaces of finite type, the DTC coincides with the FDTC.
Peter Feller +2 more
wiley +1 more source
Quotients of the Artin braid groups and crystallographic groups
, 2015 Let n be greater than or equal to 3. We study the quotient group B\_n/[P n,P\_n] of the Artin braid group B\_n by the commutator subgroup of its pure Artin braid group P\_n. We show that B\_n/[P n,P\_n] is a crystallographic group, and in the case n=3, we analyse explicitly some of its subgroups.
Gonçalves, Daciberg Lima +2 more
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Virtual planar braid groups and permutations
, 2023 Twin groups and virtual twin groups are planar analogues of braid groups and virtual braid groups, respectively. These groups play the role of braid groups in the Alexander-Markov correspondence for the theory of stable isotopy classes of immersed ...
Naik, Tushar Kanta +2 more
core +1 more source
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
wiley +1 more source
An Artin relation of length n in the braid group
Discrete Mathematics, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Braid groups and right angled Artin groups
, 2004 The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that this braid group is a right angled Artin group if X is planar.
Connolly, Frank, Doig, Margaret
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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
wiley +1 more source
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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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
wiley +1 more source