Results 51 to 60 of about 3,993 (104)

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, David E. V. Rose, Paul Wedrich   +2 more
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

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

Algebraic & Geometric Topology, 2019
14 ...
openaire   +3 more sources

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, Susanna Fishel, Christophe Hohlweg, Alice Mark   +3 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
openaire   +3 more sources

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
openaire   +2 more sources

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
wiley   +1 more source

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

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

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.
openaire   +3 more sources