Results 51 to 60 of about 3,969 (116)

Commensurability invariance for abelian splittings of right-angled Artin groups, braid groups and loop braid groups [PDF]

Algebraic & Geometric Topology, 2019
14 ...
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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, Byung Chun Kim, Yongjin Song   +2 more
wiley   +1 more source

Membership problems in braid groups and Artin groups

Journal of the London Mathematical Society
Abstract We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the nonexistence of certain forbidden‐induced subgraphs of the defining graph.
Gray, Robert D., Nyberg-Brodda, Carl-Fredrik   +1 more
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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, Guaschi, John, Ocampo, Oscar   +2 more
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A quotient of the Artin braid groups related to crystallographic groups

Journal of Algebra, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lima Gonçalves, Daciberg, Guaschi, John, Ocampo, Oscar   +2 more
openaire   +2 more sources

Unified invariant of knots from homological braid action on Verma modules

Proceedings of the London Mathematical Society, Volume 128, Issue 5, May 2024.
Abstract We re‐build the quantum sl(2)${\mathfrak {sl}(2)}$ unified invariant of knots F∞$F_{\infty }$ from braid groups' action on tensors of Verma modules. It is a two variables series having the particularity of interpolating both families of colored Jones polynomials and ADO polynomials, that is, semisimple and non‐semisimple invariants of knots ...
Jules Martel, Sonny Willetts
wiley   +1 more source

Minimal generating and normally generating sets for the braid and mapping class groups of the disc, the sphere and the projective plane

, 2012
We consider the (pure) braid groups B_{n}(M) and P_{n}(M), where M is the 2-sphere S^2 or the real projective plane RP^2. We determine the minimal cardinality of (normal) generating sets X of these groups, first when there is no restriction on X, and ...
Gonçalves, Daciberg Lima, Guaschi, John
core   +3 more sources

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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Path integral representation of the Artin braid group

Physics Letters B, 1991
Abstract Using Feynman kernels, a representation of the Artin braid group is explicitly constructed. The Schrodinger equations associated to the kernels turn out to be intimately related to the Knizhnik-Zamolodchikov equations. The representation space includes the space of correlation functions of the Wess-Zumino-Witten models.
Lai, C.H., Ting, C.
openaire   +2 more sources

Cohomology of affine Artin groups and applications

, 2007
The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients.
Callegaro, Filippo, Moroni, Davide, Salvetti, Mario   +2 more
core   +1 more source