相关论文: Free-by-cyclic groups, automorphisms and actions o…

We prove that cyclic subgroup separability is preserved under exponential completion for groups that belong to a class that includes all coherent RAAGs and toral relatively hyperbolic groups; we do so by exploiting the structure of these…

Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…

The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group.…

The present paper constructs unbounded quasimorphisms that are invariant under all automorphisms on free products of more than two factors and on graph products of finitely generated abelian groups. This includes many classes of right…

For a finite alphabet $\mathcal{A}$ and shift $X\subseteq\mathcal{A}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group ${\rm Aut}(X)$. For such systems, we…

In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…

The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…

We construct quasi-isometry invariants of a one-ended finitely presented group by considering the tree of cylinders of a two-ended JSJ decomposition of the group. When the group satisfies additional quasi-isometric rigidity hypotheses we…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial: $C_G(F)=1$. In this situation various properties of $G$ are shown to be…

It is known that an automorphism group of a K3 surface with Picard number two is either infinite cyclic group or infinite dihedral group if it is infinite. In this paper, we study the generators of an automorphism group. We use the…

We study the automorphism groups attached to a free algebra with multiple, possibly infinitely many, composition laws. As an application, we prove that the automorphism group of finitely generated vertex algebras over noetherian rings are…

We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acts absolutely non-freely on the boundary of the…

A new infinite series of rational affine algebraic varieties is constructed whose automorphism group contains the automorphism group ${\rm Aut}(F_n)$ of the free group $F_n$ of rank $n$. The automorphism groups of such varieties are…

We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base…

We study actions of finitely generated groups on $\bbR$-trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

The object of this expository work is to try to unveil the topological/geometric intuition behind the theory of free groups and their automorphism and outer automorphism groups. The method we follow is to focus on a series of problems in…

A group is called $\Lambda$-free if it has a free Lyndon length function in an ordered abelian group $\Lambda$, which is equivalent to having a free isometric action on a $\Lambda$-tree. A group has a regular free length function in…

Consider a group G and an epimorphism u_0:G\to\Z inducing a splitting of G as a semidirect product ker(u_0)\rtimes_\varphi\Z with ker(u_0) a finitely generated free group and \varphi\in Out(ker(u_0)) representable by an expanding…

We study finite groups of automorphisms of the $p$-adic open disk. In particular, we generalize results of Green, Matignon and Henrio from cyclic groups of order $p$ to arbitrary finite groups. As an application, we produce a counterexample…