Results 31 to 40 of about 3,969 (116)
Coxeter transformation groups and reflection arrangements in smooth manifolds [PDF]
, 2015 Artin groups are a natural generalization of braid groups and are well-understood in certain cases. Artin groups are closely related to Coxeter groups.
Das, Ronno, Deshpande, Priyavrat
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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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Some subgroups of Artin's braid group
Topology and its Applications, 1997 The braid group \(B_n\) has the presentation \[ \langle\sigma_1,\dots,\sigma_{n-1};\;\sigma_i=\sigma_j\;(|i-j|>1),\;\sigma_i\sigma_j\sigma_i=\sigma_j\sigma_i\sigma_j\;(|i-j|=1)\rangle. \] Let \(S_n\) denote the group of permutations of the set \(A_n=\{1,\dots,n\}\). There exists the standard homomorphism \(h\colon B_n\to S_n\), such that \(h(\sigma_i)=(
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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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Surgery groups of the fundamental groups of hyperplane arrangement complements
, 2011 Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular, for the Artin ...
A. Bartels +12 more
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Almost-crystallographic groups as quotients of Artin braid groups
Journal of Algebra, 2019 Let $n, k \geq 3$. In this paper, we analyse the quotient group $B\_n/ \_k(P\_n)$ of the Artin braid group $B\_n$ by the subgroup $ \_k(P\_n)$ belonging to the lower central series of the Artin pure braid group $P\_n$. We prove that it is an almost-crystallographic group. We then focus more specifically on the case $k=3$. If $n \geq 5$, and if $ \in
Daciberg Lima Gonçalves +2 more
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Structure theorems for braided Hopf algebras
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley +1 more source
Artin braid groups and spin structures
, 2021 We study the action of the Artin braid group B_{2g+2} on the set of spin structures on a hyperelliptic curve of genus g, which reduces to that of the symmetric group. It has been already described in terms of the classical theory of Riemann surfaces.
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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
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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