Results 41 to 50 of about 321 (123)
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 +3 more
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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Topological Complexity of Configuration Spaces [PDF]
, 2010 In this thesis we study the homotopy invariant TC(X); the topological complexity of a space X. This invariant, introduced by Farber in [15], was originally motivated by a problem in Robotics; the motion planning problem.
COSTA, ARMINDO,EMANUEL +1 more
core
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∞+$\operatorname{B}\phi ^{+}: \operatorname{B}B_{\infty }^{+} \rightarrow \operatorname{B}\Gamma _ ...
Wonjun Chang +2 more
wiley +1 more source
COMPLETING ARTIN'S BRAID GROUP ON INFINITELY MANY STRANDS [PDF]
Journal of Knot Theory and Its Ramifications, 2005 A generalization of the topological fundamental group is developed in order to construct a completion of Artin's braid group on infinitely many strands with respect to the following notion of convergence: bn → id iff for each M > 0, eventually the first M strands of bn are trivial.
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Unified invariant of knots from homological braid action on Verma modules
Proceedings of the London Mathematical Society, Volume 128, Issue 5, May 2024.Abstract We re‐build the quantum sl(2)${\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
Computation of centralizers in braid groups and Garside groups [PDF]
, 2003 We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9] Franco, N. and Gonzalez-Meneses, J.
González-Meneses López, Juan +2 more
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Virtually cocompactly cubulated Artin-Tits groups
, 2021 25 pages, 6 figures. Now includes the "virtual" part in the main resultInternational audienceWe give a complete classification of virtually cocompactly cubulated Artin-Tits groups (i.e. having a finite index subgroup acting geometrically on a CAT(0) cube
Haettel, Thomas
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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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