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 |
Acceso al artículo completo |