Geodesic
Morita classes in the homology of $\mathrm{Aut}(F_n)$ vanish after one stabilization
James Conant1 ; Karen Vogtmann2
1University of Tennessee, Knoxville, United States
2University of Warwick, Coventry, United Kingdom
Groups, geometry, and dynamics, Tome 2 (2008) no. 1, pp. 121-138

Voir la notice de l'article provenant de la source EMS Press

There is a series of cycles in the rational homology of the groups Out(Fn​), first discovered by S. Morita, which have an elementary description in terms of finite graphs. The first two of these give nontrivial homology classes, and it is conjectured that they are all nontrivial. These cycles have natural lifts to the homology of Aut(Fn​), which is stably trivial by a recent result of Galatius. We show that in fact a single application of the stabilization map Aut(Fn​)→Aut(Fn+1​) kills the Morita classes, so that they disappear immediately after they appear.
DOI : 10.4171/ggd/33
Classification : 20-XX, 00-XX
Mots-clés : Automorphism groups of free groups, Morita classes

James Conant  1   ; Karen Vogtmann  2

1 University of Tennessee, Knoxville, United States
2 University of Warwick, Coventry, United Kingdom 
James Conant; Karen Vogtmann. Morita classes in the homology of $\mathrm{Aut}(F_n)$ vanish after one stabilization. Groups, geometry, and dynamics, Tome 2 (2008) no. 1, pp. 121-138. doi: 10.4171/ggd/33
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