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