Related papers: Depth of free-by-cyclic groups

A main result is that, roughly, a dense set of the infinitesimal trace-preserving deformations of a semicircular system $s_1,..., s_n$ arise from one-parameter groups of automorphisms of the free-group factor $L(F(n))$ generated by…

Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding…

The homology groups of the automorphism group of a free group are known to stabilize as the number of generators of the free group goes to infinity, and this paper relativizes this result to a family of groups that can be defined in terms…

We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…

We present an effective algorithm for detecting automorphic orbits in free groups, as well as a number of algorithmic improvements of train tracks for free group automorphisms.

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…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

Motivated by the study of the conjugacy problem for outer automorphism of free groups, we develop the algorithmic theory of the free-by-cyclic group produced by unipotent linearly growing automorphisms of f.g. free groups. We compute…

Thurston introduced $\si_d$-invariant laminations (where $\si_d(z)$ coincides with $z^d:\ucirc\to \ucirc$, $d\ge 2$). He defined \emph{wandering $k$-gons} as sets $\T\subset \ucirc$ such that $\si_d^n(\T)$ consists of $k\ge 3$ distinct…

We develop nilpotently $p$-localization of knot groups in terms of the (symplectic) automorphism groups of free nilpotent groups. We show that any map from the set of conjugacy classes of the outer automorphism groups yields a knot…

We study so called weakly-periodic twisted-multiplicative automorphisms of the free skew-field. In particular, we show that any automorphism of a free skew-field that is defined by a periodic automorphism of a free group is equivalent to a…

Given a finite rank free group $\mathbb{F}$ of $\mathsf{rank}(\mathbb{F})\geq 3$, we show that the mapping torus of $\phi$ is (strongly) relatively hyperbolic if $\phi$ is exponentially growing. We combine our result with the work of…

Let $G = H_1 * ... * H_k * F_r$ be a torsion-free group and $\phi$ an automorphism of $G$ that preserves this free factor system. We show that when $\phi$ is fully irreducible and atoroidal relative to this free factor system, the mapping…

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger…

This paper is devoted to the proof of the property of order separability for free product of free groups with maximal cyclic amalgamated subgroups.

Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus…

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…

The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial…

We show that, for pairs of hyperbolic toral automorphisms on the $2$-torus, the points with dense forward orbits under one map and nondense forward orbits under the other is a dense, uncountable set. The pair of maps can be noncommuting. We…

The main result of this paper is that the outer automorphism group of a free product of finite groups and cyclic groups is semistable at infinity (provided it is one ended) or semistable at each end. In a previous paper, we showed that the…