Results 31 to 40 of about 3,993 (104)
The lower central and derived series of the braid groups of the sphere and the punctured sphere [PDF]
, 2006 Our aim is to determine the lower central series (LCS) and derived series (DS) for the braid groups of the sphere and of the finitely-punctured sphere. We show that for all n (resp. all n\geq 5), the LCS (resp.
Gonçalves, Daciberg Lima, Guaschi, John
core +4 more sources
Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation [PDF]
Computer Science Journal of Moldova, 2011 A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin ...
V. Kantser
doaj
Intersection of parabolic subgroups in Euclidean braid groups: a short proof
Comptes Rendus. MathématiqueWe give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group
Cumplido, María +2 more
doaj +1 more source
Graph 4-braid groups and Massey products [PDF]
, 2014 We first show that the braid group over a graph topologically containing no $\Theta$-shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and triple Massey products, we prove that a graph topologically contains ...
Hyo +3 more
core +1 more source
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.
openaire +3 more sources
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)=(
openaire +2 more sources
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
openaire +2 more sources
Elementary equivalence in Artin groups of finite type
, 2018 Irreducible Artin groups of finite type can be parametrized via their associated Coxeter diagrams into six sporadic examples and four infinite families, each of which is further parametrized by the natural numbers.
Kabiraj, Arpan +2 more
core +1 more source
Skein theory for the Links–Gould polynomial
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Building further on work of Marin and Wagner, we give a cubic braid‐type skein theory of the Links–Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list of polynomial invariants that can be computed by skein theory. As a consequence, we prove that this skein
Stavros Garoufalidis +5 more
wiley +1 more source
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
core +1 more source