## Tuesday Seminar on Topology

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

### 2008/07/01

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

On the Johnson homomorphisms of the automorphism group of
a free metabelian group
[ Abstract ]
The main object of our research is the automorphism group of a
free group. To be brief, the Johnson homomorphisms are studied in order to
describe one by one approximations of the automorphism group of a free group
. They play important roles on the study of the homology groups of the autom
orphism group of a free group. In general, to determine their images are ver
y difficult problem. In this talk, we define the Johnson homomorphisms of th
e automorphism group of a free metabelian group, and determine their images.
Using these results, we can give a lower bound on the image of the Johnson
homomorphisms of the automorphism group of a free group.