Related papers: Twisting out fully irreducible automorphisms

Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and…

A conjecture of Berkovich asserts that every non-simple finite p-group has a non-inner automorphism of order p. This conjecture is far from being proved despite the great effort devoted to it. In this paper we prove it for p-groups of…

H. Masur and J. Smillie proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher ask: Is each connected, simplicial,…

The aim of this paper is to survey some known results about mapping class group quotients by powers of Dehn twists, related to their finite dimensional representations and to state some open questions. One can construct finite quotients of…

We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the…

Classical work of Thurston and Gabai shows that finitely many taut sutured manifold hierarchies determine the Thurston norm of a compact oriented irreducible $3$-manifold with toroidal boundary. We give an explicit procedure to extract this…

We consider the question of extending a smooth homotopy coherent finite cyclic group action on the boundary of a smooth 4-manifold to its interior. As a result, we prove that Dehn twists along any Seifert homology sphere, except the…

We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: t\^ete-\`a-t\^ete graphs and twists. We completely characterize mapping…

We will survey the work on the topology of $Out(F_n)$ in the last 20 years or so. Much of the development is driven by the tantalizing analogy with mapping class groups. Unfortunately, $Out(F_n)$ is more complicated and less well-behaved.…

We show that all finitely generated free-by-cyclic groups are conjugacy separable: if a finitely generated group $G$ surjects onto $\mathbb{Z}$ with free kernel, then for every pair of non-conjugate elements $g,h\in G$, there exists a…

Let $\overline G$ be the wonderful compactification of a simple affine algebraic group $G$ of adjoint type defined over $\mathbb C.$ Let ${\overline T}\subset \overline G$ be the closure of a maximal torus $T\subset G.$ We prove that the…

We show that the number of twisted conjugacy classes is infinite for any automorphism of non-elementary, Gromov hyperbolic group . An analog of Selberg theory for twisted conjugacy classes is proposed.

In the 1970s Stallings showed that one could learn a great deal about free groups and their automorphisms by viewing the free groups as fundamental groups of graphs and modeling their automorphisms as homotopy equivalences of graphs.…

We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely…

We study the behavior of hyperbolic affine automorphisms of a translation surface which is infinite in area and genus that is obtained as a limit of surfaces built from regular polygons studied by Veech. We find that hyperbolic affine…

In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non superlinear, we prove that the automorphism group is, modulo…

Let f be a Z/2Z-spin structureon a closed surface S of genus g>3. We determine a generating set of the stabilizer of f in the mapping class group of S consisting of Dehn twists about an explicit collection of 2g+1 curves in S. If g=3 then…

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of (0,-2)-curves on threefolds, or…

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general…

We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner's construction lie off the unit circle. As a consequence, we show that for all but a few exceptional surfaces, there are examples of…