相关论文: The nonexistence of expansive polycyclic group act…

We construct a finitely presented, infinite, simple group that acts by homeomorphisms on the circle, but does not admit a non-trivial action by $C^1$-diffeomorphisms on the circle. The group emerges as a group of piecewise projective…

We show that if $G$ is a finitely generated group of subexponential growth and $X$ is a Suslinian continuum, then any action of $G$ on $X$ cannot be expansive.

In this paper we consider symplectic 4-manifolds $(M,\omega)$ with $c_1(M,\omega)=0$ which admit a Hamiltonian $S^1$-action together with an equivariant Maslov condition on orbits of the group action. We call such spaces {\em special…

We show that there are no Anosov actions by (n-1)-dimensional unimodular Lie groups on closed n-dimensional manifolds.

In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that "generic" finitely generated groups have no smooth volume preserving actions on compact manifolds…

We prove that there is no entire transcendental function in class S with real multipliers of all repelling periodic orbits.

We show that a $C^1$-generic expanding map of the circle has no absolutely continuous invariant $\sigma$-finite measure.

We show that there are no normally contracting actions of unimodular Lie groups on closed manifolds.

We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies…

We show that the fundamental group of Symp(M,w) can be nontrivial for M that does not admit any symplectic circle action.

Let $T$ be a compact fibered $3$--manifold, presented as a mapping torus of a compact, orientable surface $S$ with monodromy $\psi$, and let $M$ be a compact Riemannian manifold. Our main result is that if the induced action $\psi^*$ on…

The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth $S^1$-action vanishes. In the present work we prove a version of this result for the integral foliated simplicial volume of aspherical…

Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C^1 action of the mapping class group of S on the circle is trivial. The techniques used in the proof of…

In this partly expository monograph we develop a general framework for producing uncountable families of exotic actions of certain classically studied groups acting on the circle. We show that if $L$ is a nontrivial limit group then the…

We prove that closed symplectic four-manifolds do not admit any smooth free circle actions with contractible orbits, without assuming that the actions preserve the symplectic forms. In higher dimensions such actions by symplectomorphisms do…

We explore transformation groups of manifolds of the form $M\times S^n$, where $M$ is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finite group. In particular, we prove that for $n=2$ there exists…

The group SL(3,Z) cannot act (faithfully) on the circle (by homeomorphisms). We will see that many other arithmetic groups also cannot act on the circle. The discussion will involve several important topics in group theory, such as ordered…

We will give an example of a smooth free action of $S^1=U(1)$ on $S^7$ whose orbits have unbounded lenghts (equivalently: unbounded periods). As an application of this example we construct a $C^{\infty}$ vector field $X$, defined in a…

We show that the group of piecewise linear homeomorphisms of any compact PL manifold does not admit a Polish group topology. This uses a) new results on the relationship between topologies on groups of homeomorphisms, their algebraic…

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…