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

Clay M, Pettet A. Current twisting and nonsingular matrices. Comment. Math. Helv. 87 (2012), 385-407. doi: 10.4171/CMH/257