Calculating the image of the second Johnson-Morita representation

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dc.creatorBirman, Joan S.
dc.creatorBrendle, Tara E.
dc.creatorBroaddus, Nathan
dc.date2007-08-28
dc.date.accessioned2026-07-07T08:26:18Z
dc.date.available2026-07-07T08:26:18Z
dc.descriptionJohnson 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.
dc.description11 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0708.3861
dc.identifierhttp://arxiv.org/abs/0708.3861
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136897
dc.subjectGeometric Topology
dc.titleCalculating the image of the second Johnson-Morita representation
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