Commentarii Mathematici Helvetici

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Volume 87, Issue 2, 2012, pp. 385–407
DOI: 10.4171/CMH/257

Current twisting and nonsingular matrices

Matt T. Clay (1) and Alexandra Pettet (2)

(1) Department of Mathematics, Allegheny College, PA 16335, MEADVILLE, UNITED STATES
(2) Department of Mathematics, University of British Columbia, BC V6T 1Z2, VANCOUVER, CANADA

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

Keywords: Free groups, automorphisms, Dehn twists