Related papers: Which finite groups act smoothly on a given $4$-ma…

Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational…

In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism group of the fundamental group of a closed connected aspherical manifold $M$, we prove that the…

If $X$ is a smooth manifold and ${\mathcal{G}}$ is a subgroup of $Diff(X)$ we say that $(X,{\mathcal{G}})$ has the almost fixed point property if there exists a number $C$ such that for any finite subgroup $G\leq{\mathcal{G}}$ there is some…

We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct…

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times...\times \bbS^{n_k}$ for some…

It is a consequence of the classical Jordan bound for finite subgroups of linear groups that in each dimension n there are only finitely many finite simple groups which admit a faithful, linear action on the n-sphere. In the present paper…

Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M,…

Let $X$ be a non-uniruled compact K\"ahler space of dimension 3. We show that the group of bimeromorphic automorphisms of $X$ is Jordan. More generally, the same result holds for any compact K\"ahler space admitting a quasi-minimal model.

We show that a finite group which admits a faithful, smooth, orientation-preserving action on a homology 4-sphere, and in particular on the 4-sphere, is isomorphic to a subgroup of the orthogonal group SO(5), by explicitly determining the…

For any symplectic form $\omega$ on $T^2\times S^2$ we construct infinitely many nonisomorphic finite groups which admit effective smooth actions on $T^2\times S^2$ that are trivial in cohomology but which do not admit any effective…

This paper initiated an investigation on the following question: Suppose a smooth 4-manifold does not admit any smooth circle actions. Does there exist a constant $C>0$ such that the manifold support no smooth $\Z_p$-actions of prime order…

We classify the possible elementary amenable fundamental groups of compact aspherical 4-manifolds with boundary and conclude that they are either polycyclic or solvable Baumslag- Solitar. Since these groups are good and satisfy the…

In previous work, all finite simple groups that act with fixity 4 have been classified. In this article we investigate which ones of these groups act faithfully on a compact Riemann surface of genus at least 2 with fixity four in total and…

Let $\mathcal C$ be a set of finite groups which is closed under taking subgroups and let $d$ and $M$ be positive integers. Suppose that for any $G\in\mathcal C$ whose order is divisible by at most two distinct primes there exists an…

Riera proved at arXiv:1412.6964 that the diffeomorphism group of particular compact manifolds are not Jordan by exhibiting subgroups isomorphic to extra-special $p$-groups of exponent $p$ for primes $p$ satisfying some conditions.…

We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational…

We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…

Around twenty years ago Ghys conjectured that finite subgroups of the diffeomorphism group of a compact smooth manifold M have an abelian normal subgroup of index at most a(M), where a(M) depends only on M. First we construct a family of…

In a previous work it is shown that every finite group $G$ of diffeomorphisms of a connected smooth manifold $M$ of dimension $\geq 2$ equals, up to quotient by the flow, the centralizer of the group of smooth automorphisms of a…

A group $G$ is called Jordan if there is a positive integer $J=J_G$ such that every finite subgroup $\mathcal{B}$ of $G$ contains a commutative subgroup $\mathcal{A}\subset \mathcal{B}$ such that $\mathcal{A}$ is normal in $\mathcal{B}$ and…