Related papers: On non-isomorphic universal sofic groups

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We prove a version of the Thom Isotopy Theorem for nonproper semialgebraic maps $f\colon X\rightarrow \mathbb{R}^m$, where $X \subset\mathbb{R}^n$ is a semialgebraic set and $f$ is the restriction to $X$ of a smooth semialgebraic map…

We show that Baumslag-Solitar groups are virtually 2-avoidable, that is, they admit finite index subgroup whose first homology is devoid of $\mathbb{Z}_2$ summand. We also prove virtual 2-avoidability for some other classes of one-relator…

The Torelli group of $W_g = \#^g S^n \times S^n$ is the subgroup of the diffeomorphisms of $W_g$ fixing a disc which act trivially on $H_n(W_g;Z)$. The rational cohomology groups of the Torelli group are representations of an arithmetic…

For $p>2$, B. Simon\cite{Simon} studied the unboundedness of the Weyl transform for symbol belonging to $L^p({\mathbb{R}^n\times \mathbb{R}^n})$. In this article, we study the analog of unboundedness of the Weyl transform on some…

We show that if $M$ is a compact oriented surface of genus 0 and $G$ is a subgroup of $\Symp^\omega_\mu(M)$ which has an infinite normal solvable subgroup, then $G$ is virtually abelian. In particular the centralizer of an infinite order $f…

We prove a global topological rigidity theorem for locally $C^2$-non-discrete subgroups of the group of real analytic diffeomorphisms of the circle.

In this work we construct Calabi quasi-morphisms on the universal cover of the group Ham(M) of Hamiltonian diffeomorphisms for some non-monotone symplectic manifolds. This complements a result by Entov and Polterovich which applies in the…

A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic…

It is shown that any finitely generated non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This settles in the affirmative a conjecture of Graham Higman.

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

A real algebraic variety is maximal (with respect to the Smith-Thom inequality) if the sum of the Betti numbers (with $\mathbb{Z}_2$ coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We…

We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These…

We classify a large class of small groups of finite Morley rank: $N_\circ^\circ$-groups which are the infinite analogues of Thompson's $N$-groups. More precisely, we constrain the $2$-structure of groups of finite Morley rank containing a…

We prove that each infinite 2-group with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group or to the infinite group of generalized quaternions.

In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.

As a result of impressive research arXiv:2106.07231, D. Garc\'{\i}a-Lucas, \'{A}. del R\'{i}o and L. Margolis defined an infinite series of non-isomorphic $2$-groups $G$ and $H$, whose group algebras $\mathbb{F}G$ and $\mathbb{F}H$ over the…

We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.

We prove a statement of Ax-Lindemann type for the uniformization of products of Mumford curves whose associated fundamental groups are non-abelian Schottky subgroups of $\mathop{\rm PGL}(2,\bar{\mathbf Q_p})$ contained in $\mathop{\rm…

We define an algebra $\mathcal{U}_0$ using a simplified set of generators for the quantum toroidal algebra $U_q(sl_{n+1}, tor)$ and show that there exists an epimorphism from $\mathcal{U}_0$ to $U_q(sl_{n+1}, tor)$. We derive a closed…