Results 51 to 60 of about 104 (85)

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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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

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

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

Algebraic & Geometric Topology, 2019
We prove that if a right-angled Artin group $A_Γ$ is abstractly commensurable to a group splitting non-trivially as an amalgam or HNN-extension over $\mathbb{Z}^n$, then $A_Γ$ must itself split non-trivially over $\mathbb{Z}^k$ for some $k\le n$. Consequently, if two right-angled Artin groups $A_Γ$ and $A_Δ$ are commensurable and $Γ$ has no separating $
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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.
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Formal derivation of the Laughlin function and its generalization for other topological phases of FQHE. [PDF]

Sci Rep, 2022
Jacak JE.
europepmc   +1 more source

Perverse schobers and Orlov equivalences. [PDF]

Eur J Math, 2023
Koseki N, Ouchi G.
europepmc   +1 more source

Topological complexity of subgroups of Artin's braid groups

, 2016
v2: 12 pages, added Section 6 on higher topological ...
Grant, Mark, Recio-Mitter, David
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Examples of centralizers in the Artin braid groups

, 2003
The goal of this paper is to construct examples of centralizers in the Artin braid groups requiring the number of generators quadratic in the number of strings. These examples disprove a recent conjecture of N. Franco and J. Gonzalez-Meneses.
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Flat braid groups, right-angled Artin groups, and commensurability

Pacific Journal of Mathematics
27 pages, 11 figures. Comments are welcome!
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