Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.

Jensen, Craig A.. "Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.." Publicacions Matemàtiques 46.1 (2002): 97-118. <http://eudml.org/doc/41445>.

@article{Jensen2002,
abstract = {It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);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(Q'm; Z), H6(Q'm; Z), and H5(Qm; Z) never stabilize as m → ∞, where the moduli spaces Q'm and Qm are the quotients of the spines X'm and Xm of “outer space” and “auter space”, respectively, introduced in [3] by Culler and Vogtmann and [6] by Hatcher and Vogtmann.},
author = {Jensen, Craig A.},
journal = {Publicacions Matemàtiques},
keywords = {Cohomología de grupos; Grupos de automorfismos; Grupos libres; Espacio de Moduli; Teoría de grafos; stable rational cohomology groups; integral cohomology; moduli spaces of pointed graphs; groups of outer automorphisms; free groups},
language = {eng},
number = {1},
pages = {97-118},
title = {Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.},
url = {http://eudml.org/doc/41445},
volume = {46},
year = {2002},
}

TY - JOUR
AU - Jensen, Craig A.
TI - Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
JO - Publicacions Matemàtiques
PY - 2002
VL - 46
IS - 1
SP - 97
EP - 118
AB - It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);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(Q'm; Z), H6(Q'm; Z), and H5(Qm; Z) never stabilize as m → ∞, where the moduli spaces Q'm and Qm are the quotients of the spines X'm and Xm of “outer space” and “auter space”, respectively, introduced in [3] by Culler and Vogtmann and [6] by Hatcher and Vogtmann.
LA - eng
KW - Cohomología de grupos; Grupos de automorfismos; Grupos libres; Espacio de Moduli; Teoría de grafos; stable rational cohomology groups; integral cohomology; moduli spaces of pointed graphs; groups of outer automorphisms; free groups
UR - http://eudml.org/doc/41445
ER -