Geometry & Topology Monographs 13 (2008) 147–168

DOI: 10.2140/gtm.2008.13.147

arXiv: math.AT/0610946

Abstract

Let F_n = ⟨x₁, …, x_n⟩ denote the free group with generators {x₁, …, x_n}. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F_n to the general linear group over the integers. In particular among them are the automorphisms χ_k,i which conjugate the generator x_k by the generator x_i leaving the x_j fixed for j not k. A computation of the cohomology ring as well as the Lie algebra obtained from the descending central series of the group generated by χ_k,i for i < k is given here. Partial results are obtained for the group generated by all χ_k,i.

Keywords

automorphism group, free group, basis-conjugating automorphism, Lie algebra, cohomology

Mathematical Subject Classification

Primary: 20F28

Secondary: 20F40, 20J06

References

Publication

Received: 31 May 2006
Revised: 6 March 2007
Accepted: 13 March 2007
Published: 22 February 2008

Authors