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Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs
Jensen, Craig A.

Data: 2002
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions matematiques, V. 46 N. 1 (2002) , p. 97-118, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_46102_06
DOI: 10.5565/38046

22 p, 1.1 MB

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