| Abstract: |
It is not known whether or not the stable rational cohomology groups H*(Aut(F[infinity]);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields that H5(Qm; Z), H6(Qm; Z), and H5(Qm; Z) never stabilize as m --> [infinity], where the moduli spaces ^Qm and Qm are the quotients of the spines ^Xm and Xm of "outer space" and "auter space", respectively, introduced in [3] by Culler and Vogtmann and [6] by Hatcher and Vogtmann. |
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