The co-Hopfian property of the Johnson kernel and the Torelli group

Details The co-Hopfian property of the Johnson kernel and the Torelli group The co-Hopfian property of the Johnson kernel and the Torelli group

2009-11-20

arxiv.org/abs/0911.3923v6

Mathematics

Group Theory

24 pages, 8 figures

Scientific paper

For all but finitely many compact orientable surfaces, we show that any
superinjective map from the complex of separating curves into itself is induced
by an element of the extended mapping class group. We apply this result to
proving that any finite index subgroup of the Johnson kernel is co-Hopfian.
Analogous properties are shown for the Torelli complex and the Torelli group.

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