Current twisting and nonsingular matrices

  • Matt T. Clay

    Allegheny College, Meadville, United States
  • Alexandra Pettet

    University of British Columbia, Vancouver, Canada


We show that for k3k \geq 3, given any matrix in GL(k,Zk,\mathbb{Z}), there is a hyperbolic fully irreducible automorphism of the free group of rank kk whose induced action on Zk\mathbb{Z}^k is the given matrix.

Cite this article

Matt T. Clay, Alexandra Pettet, Current twisting and nonsingular matrices. Comment. Math. Helv. 87 (2012), no. 2, pp. 385–407

DOI 10.4171/CMH/257