English

Stable homology of automorphism groups of free groups

Algebraic Topology 2008-02-18 v3 Group Theory

Abstract

Homology of the group Aut(F_n) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prove that in this range it agrees with homology of symmetric groups. In particular, Aut(F_n) has no stable rational homology, settling a conjecture of Hatcher and Vogtmann.

Keywords

Cite

@article{arxiv.math/0610216,
  title  = {Stable homology of automorphism groups of free groups},
  author = {Soren Galatius},
  journal= {arXiv preprint arXiv:math/0610216},
  year   = {2008}
}

Comments

60 pages; 3 figures; v3 has a few typos fixed (one is in definition 2.4(i))