Results 71 to 80 of about 5,391,081 (192)

The last incoherent Artin group [PDF]

Proceedings of the American Mathematical Society, 2012
The author studies the (in)coherence of certain \(3\)-generator Artin groups. Recall that a group is called coherent if every finitely generated subgroup is finitely presented. In the author's notation, we write \(A(pqr)\) for the Artin group generated by three elements which, when cyclically ordered, satisfy Artin relations of length \(p\), \(q\) and \
openaire   +2 more sources

Motivic mirror symmetry and χ$\chi$‐independence for Higgs bundles in arbitrary characteristic

Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.
Abstract We prove that the (twisted orbifold) motives of the moduli spaces of SLn$\mathrm{SL}_n$ and PGLn$\mathrm{PGL}_n$‐Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is invertible are isomorphic in Voevodsky's triangulated category of motives.
Victoria Hoskins, Simon Pepin Lehalleur
wiley   +1 more source

Braided finite automata and representation theory

Nuclear Physics B
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter’s groups and the associated word problem, we turn to the Artin ...
Anastasia Doikou
doaj   +1 more source

Thurston norm for coherent right‐angled Artin groups via L2$L^2$‐invariants

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We define a new notion of splitting complexity for a group G$G$ along a non‐trivial integral character ϕ∈H1(G;Z)$\phi \in H^1(G; \mathbb {Z})$. If G$G$ is a one‐ended coherent right‐angled Artin group, we show that the splitting complexity along an epimorphism ϕ:G→Z$\phi \colon G \rightarrow \mathbb {Z}$ equals the L2$L^2$‐Euler characteristic
Monika Kudlinska
wiley   +1 more source

Random Artin groups

, 2023
We introduce a new model of random Artin groups. The two variables we consider are the rank of the Artin groups and the set of permitted coefficients of their defining graphs.
Vaskou, Nicolas, Goldsborough, Antoine
core  

On the linearity of Artin braid groups

Journal of Algebra, 2003
The author proves that all Artin groups of crystallographic type have a faithful representation of dimension the number of reflections of the associated Coxeter group. The faithfulness criterion which is used is that of \textit{D. Krammer} [Ann. Math. (2) 155, No. 1, 131-156 (2002; Zbl 1020.20025)].
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The quasi‐redirecting boundary

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi‐geodesic rays and the space is equipped with a topology that is naturally invariant under quasi‐isometries.
Yulan Qing, Kasra Rafi
wiley   +1 more source

Wild conductor exponents of curves

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We give an explicit formula for wild conductor exponents of plane curves over Qp$\mathbb {Q}_p$ in terms of standard invariants of explicit extensions of Qp$\mathbb {Q}_p$, generalising a formula for hyperelliptic curves. To do so, we prove a general result relating the wild conductor exponent of a simply branched cover of the projective line ...
Harry Spencer
wiley   +1 more source

Measure equivalence classification of right-angled Artin groups: the finite $\mathrm{Out}$ classes

Given a right-angled Artin group $G$ with finite outer automorphism group, we determine which right-angled Artin groups are measure equivalent (or orbit equivalent) to $G$
Huang, Jingyin, Horbez, Camille
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The Lp$L^p$‐diameter of the space of contractible loops

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area‐preserving diffeomorphisms endowed with the Lp$L^p$‐metric. As a special case, this resolves the Lp$L^p$‐metric analog of the well‐known question in symplectic topology ...
Michael Brandenbursky, Egor Shelukhin
wiley   +1 more source