Related papers: Continuous group actions on profinite spaces
Let F be a non-archimedean local field of characteristic zero whose residue field has at least three elements. Let G be an almost simple linear algebraic group over F, with rank_F(G) >= 2. Let X be a simply connected symmetric space of…
We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…
In this ongoing work, we extend to a class of well-behaved pre-special hyperfields the work of J. Min\'a\v c and Spira (\cite{minac1996witt}) that describes a (pro-2)-group of a field extension that encodes the quadratic form theory of a…
We study a condensed version of the \'etale homotopy type of a scheme, which refines both the usual \'etale homotopy type of Friedlander-Artin-Mazur and the pro\'etale fundamental group of Bhatt-Scholze. In the first part of this paper, we…
We prove a descent result for affine/projective varieties defined over an algebraically closed field. The idea is to work with the reduced Groebner basis of the ideal where the variety vanishes and study it's behaviour under group action…
The Roelcke precompactness of transformation groups of discrete spaces and chains in the permutation topology and LOTS in the topology of pointwise convergence is studied. For ultratransitive actions compactifications of transformation…
We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for compact effective group actions on spheres and provide…
In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in…
We consider faithful projective actions of a cocompact lattice of SL(2,R) on the projective plane, with the following property: there is a common fixed point, which is a saddle fixed point for every element of infinite order of the the…
A homogeneous space is a manifold on which a Lie group acts transitively. Super generalization of this concept is also studied in [2] and [4]. In this paper we explicitly show that super Lie group GL(m|n) acts transitively on…
It is proved that the profinite completion of the mapping class group Mod (g,n) of a surface of genus g with n boundary components is isomorphic to such of the arithmetic group GL(6g-6+2n, Z). We establish a relation between the normal…
We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the…
These notes expand upon our lectures on {\em profinite rigidity} at the international colloquium on randomness, geometry and dynamics, organised by TIFR Mumbai at IISER Pune in January 2024. We are interested in the extent to which groups…
We have defined and established a theory of cofinite connectedness of a cofinite graph. Many of the properties of connectedness of topological spaces have analogs for cofinite connectedness. We have seen that if $G$ is a cofinite group and…
We examine a moduli problem for real and quaternionic vector bundles on a smooth complex projective curve with a fixed real structure, and we give a gauge-theoretic construction of moduli spaces for semi-stable such bundles with fixed…
Let $\mathfrak C$ be a class of finite groups which is closed for subgroups, quotients and direct products. Given a profinite group $G$ and an element $x\in G$, we denote by $P_{\mathfrak{C}}(x,G)$ the probability that $x$ and a randomly…
In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…
By homotopy linear algebra we mean the study of linear functors between slices of the $\infty$-category of $\infty$-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices…
We present two examples of actions of non-regular locally compact quantum groups on their homogeneous spaces. The homogeneous spaces are defined in a way specific to these examples, but the definitions we use have the advantage of being…
In this paper, we describe the homotopy type of the homotopy fixed point sets of $S^3$-actions on rational spheres and complex projective spaces, and provide some properties of $S^1$-actions on a general rational complex.