Todor Tsankov
YOU?
Author Swipe
View article: On compact uniformly recurrent subgroups
On compact uniformly recurrent subgroups Open
Let a group Γ act on a paracompact, locally compact, Hausdorff space M by homeomorphisms and let 2 M denote the set of closed subsets of M . We endow 2 M with the Chabauty topology, which is compact and admits a natural Γ-action by homeomo…
View article: Dense and comeager conjugacy classes in zero-dimensional dynamics
Dense and comeager conjugacy classes in zero-dimensional dynamics Open
Let $G$ be a countable group. We consider the Polish space of all actions of $G$ on the Cantor space by homeomorphisms and study the existence of a comeager conjugacy class in this space and some natural subspaces. We also develop a genera…
View article: Non-singular and probability measure-preserving actions of infinite permutation groups
Non-singular and probability measure-preserving actions of infinite permutation groups Open
We prove two theorems in the ergodic theory of infinite permutation groups. First, generalizing a theorem of Nessonov for the infinite symmetric group, we show that every non-singular action of a non-archimedean, Roelcke precompact, Polish…
View article: Continuity of the stabilizer map and irreducible extensions
Continuity of the stabilizer map and irreducible extensions Open
Let G be a locally compact group. For every G -flow X , one can consider the stabilizer map x \mapsto G_{x} , from X to the space \mathrm{Sub}(G) of closed subgroups of G . This map is not continuous in general. We prove that if one passes…
View article: Extremal models and direct integrals in affine logic
Extremal models and direct integrals in affine logic Open
Affine logic is a fragment of continuous logic, introduced by Bagheri, in which only affine functions are allowed as connectives. This has the effect of endowing type spaces with the structure of compact convex sets. We study extremal mode…
View article: Continuity of the stabilizer map and irreducible extensions
Continuity of the stabilizer map and irreducible extensions Open
Let $G$ be a locally compact group. For every $G$-flow $X$, one can consider the stabilizer map $x \mapsto G_x$, from $X$ to the space $\mathrm{Sub}(G)$ of closed subgroups of $G$. This map is not continuous in general. We prove that if on…
View article: Topological dynamics of kaleidoscopic groups
Topological dynamics of kaleidoscopic groups Open
Kaleidoscopic groups are a class of permutation groups recently introduced by Duchesne, Monod, and Wesolek. Starting with a permutation group $Γ$, the kaleidoscopic construction produces another permutation group $\mathcal{K}(Γ)$ which act…
View article: CONTINUOUS LOGIC AND BOREL EQUIVALENCE RELATIONS
CONTINUOUS LOGIC AND BOREL EQUIVALENCE RELATIONS Open
We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially…
View article: Continuous logic and Borel equivalence relations
Continuous logic and Borel equivalence relations Open
We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially…
View article: Bernoulli disjointness
Bernoulli disjointness Open
International audience
View article: Invariant measures on products and on the space of linear orders
Invariant measures on products and on the space of linear orders Open
Let $M$ be an $\aleph_0$-categorical structure and assume that $M$ has no algebraicity and has weak elimination of imaginaries. Generalizing classical theorems of de Finetti and Ryll-Nardzewski, we show that any ergodic, $\operatorname{Aut…
View article: Invariant measures on products and on the space of linear orders
Invariant measures on products and on the space of linear orders Open
Let $M$ be an $\\aleph_0$-categorical structure and assume that $M$ has no\nalgebraicity and has weak elimination of imaginaries. Generalizing classical\ntheorems of de Finetti and Ryll-Nardzewski, we show that any ergodic,\n$\\operatornam…
View article: Realizing uniformly recurrent subgroups
Realizing uniformly recurrent subgroups Open
International audience
View article: Universal minimal flows of homeomorphism groups of high-dimensional\n manifolds are not metrizable
Universal minimal flows of homeomorphism groups of high-dimensional\n manifolds are not metrizable Open
Answering a question of Uspenskij, we prove that if $X$ is a closed manifold\nof dimension $2$ or higher or the Hilbert cube, then the universal minimal flow\nof $\\mathrm{Homeo}(X)$ is not metrizable. In dimension $3$ or higher, we also\n…
View article: Realizing uniformly recurrent subgroups
Realizing uniformly recurrent subgroups Open
We show that every uniformly recurrent subgroup of a locally compact group is the family of stabilizers of a minimal action on a compact space. More generally, every closed invariant subset of the Chabauty space is the family of stabilizer…
View article: Eberlein oligomorphic groups
Eberlein oligomorphic groups Open
International audience
View article: Eberlein oligomorphic groups
Eberlein oligomorphic groups Open
We study the Fourier–Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups. We characterize the family of such groups whose Fourier–St…
View article: Metrizable universal minimal flows of Polish groups have a comeagre\n orbit
Metrizable universal minimal flows of Polish groups have a comeagre\n orbit Open
We prove that, whenever $G$ is a Polish group with metrizable universal\nminimal flow $M(G)$, there exists a comeagre orbit in $M(G)$. It then follows\nthat there exists an extremely amenable, closed, coprecompact $G^*$ of $G$ such\nthat $…
View article: Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups
Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups Open
We investigate the automorphism groups of $\\aleph\\_0$-categorical structures\nand prove that they are exactly the Roelcke precompact Polish groups. We show\nthat the theory of a structure is stable if and only if every Roelcke uniformly\…
View article: Free actions of free groups on countable structures and property (T)
Free actions of free groups on countable structures and property (T) Open
We show that if $G$ is a non-archimedean, Roelcke precompact, Polish group,\nthen $G$ has Kazhdan's property (T). Moreover, if $G$ has a smallest open\nsubgroup of finite index, then $G$ has a finite Kazhdan set. Examples of such\n$G$ incl…
View article: Polish Groups with Metrizable Universal Minimal Flows
Polish Groups with Metrizable Universal Minimal Flows Open
We prove that if the universal minimal flow of a Polish group $G$ is metrizable and contains a $G_δ$ orbit $G \cdot x_0$, then it is isomorphic to the completion of the homogeneous space $G/G_{x_0}$ and show how this result translates natu…