Zobrazeno 1 - 10
of 3 138
pro vyhledávání: '"A Genevois"'
Autor:
Genevois, Anthony
It is a theorem due to F. Haglund and D. Wise that reflection groups (aka Coxeter groups) virtually embed into right-angled reflection groups (aka right-angled Coxeter groups). In this article, we generalise this observation to rotation groups, which
Externí odkaz:
http://arxiv.org/abs/2404.15652
In this article, we introduce and study a natural notion of coarse separation for metric spaces, with an emphasis on coarse separation by subspaces of polynomial or subexponential growth. For instance, we show that symmetric spaces of non-compact typ
Externí odkaz:
http://arxiv.org/abs/2401.18025
Autor:
Genevois, Anthony, Tessera, Romain
In this article, we introduce halo products as a natural generalisation of wreath products. They also encompass lampshuffler groups $\mathrm{FSym}(H) \rtimes H$ and lampcloner groups $\mathrm{FGL}(H) \rtimes H$, as well as many possible variations ba
Externí odkaz:
http://arxiv.org/abs/2401.13520
Recently, Lin and Shinder constructed non-trivial homomorphisms from Cremona groups of rank >2 to \mathbb{Z} using motivic techniques. In this short note we propose an alternative perspective from median geometry on their theorem.
Comment: 6 pag
Comment: 6 pag
Externí odkaz:
http://arxiv.org/abs/2312.05197
Autor:
Genevois, Anthony
For every $n \geq 1$, let $(\mathrm{FW}_n)$ denote the fixed-point property for median graphs of cubical dimension $n$ (or equivalently, for CAT(0) cube complexes of dimension $n$). In this article, we construct groups satisfying $(\mathrm{FW}_n)$ bu
Externí odkaz:
http://arxiv.org/abs/2311.12402
Extending Stallings' foldings of trees, we show in this article that every parallel-preserving map between median graphs factors as an isometric embedding through a sequence of elementary transformations which we call foldings and swellings. This new
Externí odkaz:
http://arxiv.org/abs/2311.09751
Autor:
Genevois, Anthony
In this note, we discuss and motivate the use of the terminology ``median graphs'' in place of ``CAT(0) cube complexes'' in geometric group theory.
Comment: 10 pages. Comments are welcome!
Comment: 10 pages. Comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2309.02070
In this article, we show that, for every $n \geq 2$, the pure virtual twin group $PVT_n$ can be naturally described as a symmetric diagram group, a family of groups introduced by V. Guba and M. Sapir and associated to semigroup presentations. Inspire
Externí odkaz:
http://arxiv.org/abs/2305.11810
Autor:
Genevois, Anthony
Given a graph $\Gamma$, the right-angled Artin group $A(\Gamma)$ is given by the presentation $\langle u \in V(\Gamma) \mid [u,v]=1, \ \{u,v\} \in E(\Gamma) \rangle$. The Embedding Problem in right-angled Artin groups asks, given two finite graphs $\
Externí odkaz:
http://arxiv.org/abs/2304.05267
We introduce Property (NL), which indicates that a group does not admit any (isometric) action on a hyperbolic space with loxodromic elements. In other words, such a group $G$ can only admit elliptic or horocyclic hyperbolic actions, and consequently
Externí odkaz:
http://arxiv.org/abs/2212.14292