# Current twisting and nonsingular matrices

@article{Clay2009CurrentTA, title={Current twisting and nonsingular matrices}, author={Matt Clay and Alexandra Pettet}, journal={arXiv: Group Theory}, year={2009} }

We show that for k at least 3, given any matrix in GL(k,Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z^k is the given matrix.

## Figures from this paper

## 16 Citations

### Twisting Out Fully Irreducible Automorphisms

- Mathematics
- 2009

By a theorem of Thurston, in the subgroup of the mapping class group generated by Dehn twists around two curves which fill, every element not conjugate to a power of one of the twists is…

### Simultaneous construction of hyperbolic isometries

- Mathematics
- 2016

Given isometric actions by a group G on finitely many \delta-hyperbolic metric spaces, we provide a sufficient condition that guarantees the existence of a single element in G that is hyperbolic for…

### Graph towers, laminations and their invariant measures

- MathematicsJournal of the London Mathematical Society
- 2020

In this paper we present a combinatorial machinery, consisting of a graph tower Γ← and vector towers v← on Γ← , which allows us to efficiently describe all invariant measures μ=μv← on any given shift…

### Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space

- Mathematics
- 2014

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection…

### DYNAMICS OF FREE GROUP AUTOMORPHISMS AND A SUBGROUP ALTERNATIVE FOR OUT(FN) BY CAGLAR UYANIK

- Mathematics
- 2017

This thesis is motivated by a foundational result of Thurston which states that pseudoAnosov mapping classes act on the compactified Teichmüller space with north-south dynamics. We prove that several…

### A positive proportion of elements of mapping class groups is pseudo‐Anosov

- Mathematics
- 2017

In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at the proportion among…

### Dynamics of hyperbolic iwips

- Mathematics
- 2014

We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of $Out(F_N)$ acts on the projectivized space of geodesic currents…

### RELATIVE TWISTING IN OUTER SPACE

- Mathematics
- 2011

Subsurface projection is indispensable to studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called…

### Spectral rigidity of automorphic orbits in free groups

- Mathematics
- 2012

It is well-known that a point T in the (unprojectivized) Culler-Vogtmann Outer space cv_N is uniquely determined by its translation length function ||.||_T : F_N → R. A subset S of a free group F_N…

### Corrigendum: “Spectral rigidity of automorphic orbits in free groups”

- Mathematics
- 2014

Lemma 5.1 in our paper [6] says that every infinite normal subgroup of Out(F_N) contains a fully irreducible element; this lemma was substantively used in the proof of the main result, Theorem A in…

## References

SHOWING 1-10 OF 37 REFERENCES

### Irreducible outer automorphisms of a free group

- Mathematics
- 1991

We give sufficient conditions for all positive powers of an outer automorphism of a finitely generated free group to be irreducible, in the sense of Bestvina and Handel. We prove a conjecture of…

### A hyperbolic Out(Fn)-complex

- Mathematics
- 2010

For any finite collection fi of fully irreducible automorphisms of the free group Fn we construct a connected i-hyperbolic Out.Fn/-complex in which each fi has positive translation length.

### Twisting Out Fully Irreducible Automorphisms

- Mathematics
- 2009

By a theorem of Thurston, in the subgroup of the mapping class group generated by Dehn twists around two curves which fill, every element not conjugate to a power of one of the twists is…

### On hyperbolic groups

- Mathematics
- 2006

Abstract We prove that a δ-hyperbolic group for δ < ½ is a free product F * G 1 * … * Gn where F is a free group of finite rank and each Gi is a finite group.

### Hyperbolic automorphisms of free groups

- Mathematics
- 1999

Abstract. We prove that an automorphism
$ {\not o} : F \to F $ of a finitely generated free group F is hyperbolic in the sense of Gromov if it has no nontrivial periodic conjugacy classes. This…

### On the Combination Theorem for Negatively Curved Groups

- MathematicsInt. J. Algebra Comput.
- 1997

We give a simple proof of a sufficient condition for an amalgamated free product of two negatively curved groups to be negatively curved, and we compute the curvature of such products.

### A hyperbolic Out(F_n)-complex

- Mathematics
- 2008

For any finite collection $f_i$ of fully irreducible automorphisms of the free group $F_n$ we construct a connected $\delta$-hyperbolic $Out(F_n)$-complex in which each $f_i$ has positive translation…

### Automorphisms of Surfaces after Nielsen and Thurston

- Mathematics
- 1988

Preface Introduction 1. The hyperbolic plane H2 2. Hyberbolic structures on surfaces 3. Geodesic laminations 4. Structure of geodesic laminations 5. Surface automorphisms 6. Pseudo-Anosov…

### Geodesic currents on negatively curved groups

- Mathematics
- 1991

A negatively curved or hyperbolic group, as introduced by M. Gromov, is a finitely generated group whose Cayley graphs asymptotically behave at infinity like a tree. Considering the action of a…

### Non-uniquely ergodic foliations of thin type

- MathematicsErgodic Theory and Dynamical Systems
- 1997

We construct a minimal foliation of thin type which is not uniquely ergodic. The notion of thin type relates to Rips' classification of foliations on 2-complexes.