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 -
