Mathematics – Geometric Topology
Scientific paper
2007-08-28
Mathematics
Geometric Topology
11 pages, 1 figure
Scientific paper
Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus $g$ with one boundary component to $\wedge^3 H$, the third exterior product of the homology of the surface. Morita then extended Johnson's homomorphism to a homomorphism from the entire mapping class group to ${1/2} \wedge^3 H \semi \sp(H)$. This Johnson-Morita homomorphism is not surjective, but its image is finite index in ${1/2} \wedge^3 H \semi \sp(H)$. Here we give a description of the exact image of Morita's homomorphism. Further, we compute the image of the handlebody subgroup of the mapping class group under the same map.
Birman Joan S.
Brendle Tara E.
Broaddus Nathan
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