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

Publicacions Matemàtiques (2002)

- Volume: 46, Issue: 1, page 97-118
- ISSN: 0214-1493

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topJensen, 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 -

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