arXiv:math/0610216 Abstract

arXiv:math/0610216 [math.AT]Abstract References Reviews Resources

Stable homology of automorphism groups of free groups

Published 2006-10-06, updated 2008-02-18Version 3

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.

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

Categories: math.AT, math.GR

Subjects: 55P42, 20J06

Keywords: free group, automorphism groups, stable homology, homotopy theory, symmetric groups

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