Stable homology of automorphism groups of free groups

Details Stable homology of automorphism groups of free groups Stable homology of automorphism groups of free groups

2006-10-06

arxiv.org/abs/math/0610216v3

Mathematics

Algebraic Topology

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

Scientific paper

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.

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