Related papers: A survey of topological Zimmer's program

This paper is a survey on the {\em Zimmer program}. In it's broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are $(1)$ to put in context the original questions and…

Let SL(n,Z) be the special linear group over integers and $M =S^r_1 \times S^r_2,T^r_1 \times S^r_2$ , or $T^r_0 \times S^r_1 \times S^r_2$, products of spheres and tori. We prove that any group action of SL(n,Z) on $M^r$ by diffeomorphims…

Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, known as the {\it Zimmer program}. When the group is too large…

In this paper we study Zimmer's conjecture for $C^1$ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the…

We prove many new cases of Zimmer's conjecture for actions by lattices in non-$\mathbb{R}$-split semisimple Lie groups $G$. By prior arguments, Zimmer's conjecture reduces to studying certain probability measures invariant under a minimal…

We classify compact K\"ahler manifolds $M$ of dimension $n\geq 3$ on which acts a lattice of an almost simple real Lie group of rank $\geq n-1$. This provides a new line in the so-called Zimmer program, and characterizes certain type of…

We consider Zimmer's program of lattice actions on surfaces by PL homomorphisms. It is proved that when the surface is not the torus or Klein bottle the action of any finite-index subgroup of SL(n,Z), n>4, (more generally for any 2-big…

We prove Zimmer's conjecture for $C^2$ actions by finite-index subgroups of $\mathrm{SL}(m,\mathbb{Z})$ provided $m>3$. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in…

In this report, we first recall the Poincar\'e's classification theorem for minimal orientation-preserving homeomorphisms on the circle and the Ghys' classification theorem for minimal orientation-preserving group actions on the circle.…

In this article we propose a metric variation on the C^0-version of the Zimmer program for three manifolds. After a reexamination of the isometry groups of geometric three-manifolds, we consider homomorphisms defined on higher rank lattices…

We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.

In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

Let $\mathrm{SL}_{n}(\mathbb{Z})$ $(n\geq 3)$ be the special linear group and $M^{r}$ be a closed aspherical manifold. It is proved that when $r<n,$ a group action of $\mathrm{SL}_{n}(\mathbb{Z})$ on $M^{r}$ by homeomorphisms is trivial if…

We find an algorithmic procedure that enables to compute and to describe the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step…

We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.

We establish finiteness of low-dimensional actions of lattices in higher-rank semisimple Lie groups and establish Zimmer's conjecture for many such groups. This builds on previous work of the authors handling the case of actions by…

We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space…

We prove a theorem of Tits type about automorphism groups for compact Kahler manifolds, which has been conjectured in the paper [KOZ].

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…