Zobrazeno 1 - 10
of 209
pro vyhledávání: '"Tessera, Romain"'
Autor:
Tessera, Romain, Tointon, Matthew
We give sharp bounds in Breuillard, Green and Tao's finitary version of Gromov's theorem on groups with polynomial growth. Precisely, we show that for every non-negative integer d there exists $c=c(d)>0$ such that if $G$ is a group with finite symmet
Externí odkaz:
http://arxiv.org/abs/2403.02485
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
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:
Tessera, Romain, Tointon, Matthew
We show that if $K\ge1$ is a parameter and $S$ is a finite symmetric subset of a group containing the identity such $|S^{2n}|\le K|S^n|$ for some integer $n\ge 2K^2$, then $|S^{3n}|\le\exp(\exp(O(K^2)))|S^n|$. Such a result was previously known only
Externí odkaz:
http://arxiv.org/abs/2310.20500
We prove various obstructions to the existence of regular maps (or coarse embeddings) between commonly studied spaces. For instance, there is no regular map (or coarse embedding) $\mathbb H^n\to\mathbb H^{n-1}\times Y$ for $n\geq 3$, or $(T_3)^n \to
Externí odkaz:
http://arxiv.org/abs/2303.01969
Autor:
Tessera, Romain, Winkel, Jeroen
We investigate fixed point properties for isometric actions of topological groups on a wide class of metric spaces, with a particular emphasis on Hilbert spaces. Instead of requiring the action to be continuous, we assume that it is ``controlled", i.
Externí odkaz:
http://arxiv.org/abs/2212.04900
Autor:
Tessera, Romain, Tointon, Matthew
We give a short geometric proof of a result of Soardi & Woess and Salvatori that a quasitransitive graph is amenable if and only if its automorphism group is amenable and unimodular. We also strengthen one direction of that result by showing that if
Externí odkaz:
http://arxiv.org/abs/2210.02867
Twin-width is a recently introduced graph parameter with applications in algorithmics, combinatorics, and finite model theory. For graphs of bounded degree, finiteness of twin-width is preserved by quasi-isometry. Thus, through Cayley graphs, it defi
Externí odkaz:
http://arxiv.org/abs/2204.12330
Belinskaya's theorem states that given an ergodic measure-preserving transformation, any other transformation with the same orbits and an $\mathrm{L}^1$ cocycle must be flip-conjugate to it. Our main result shows that this theorem is optimal: for all
Externí odkaz:
http://arxiv.org/abs/2201.06662