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

Título inglés Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
Título español Cohomología racional estable de grupos de automorfismos de grupos libres y la cohomología integral de espacios de moduli de grafos.
Autor/es Jensen, Craig A.
Organización Dep. Math. Univ. New Orleans, Nueva Orleans (Louisiana), Estados Unidos
Revista 0214-1493
Publicación 2002, 46 (1): 97-118, 14 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120106
Palabras clave español Cohomología de grupos ; Grupos de automorfismos ; Grupos libres ; Espacio de Moduli ; Teoría de grafos
Código MathReviews MR1904858
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