The Johnson homomorphism and the third rational cohomology group of the Torelli group
نویسندگان
چکیده
منابع مشابه
The Johnson homomorphism and the third rational cohomology group of the Torelli group
To study the structure of the Torelli group, the Johnson homomorphism and the representation theory of the symplectic group are essential tools. Using them, we give a lower bound for the dimension of the third rational cohomology group and a new approach to the non-triviality of characteristic classes of surface bundles on the Torelli group.
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Let Fn be the free group on n generators. Define IAn to be group of automorphisms of Fn that act trivially on first homology. The Johnson homomorphism in this setting is a map from IAn to its abelianization. The first goal of this paper is to determine how much this map contributes to the second rational cohomology of IAn . A descending central series of IAn is given by the subgroups K (i) n wh...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2005
ISSN: 0166-8641
DOI: 10.1016/j.topol.2004.08.002