Abstract
Let be the subgroup of the extended mapping class group, , generated by Dehn twists about separating curves. Assuming that is a closed, orientable surface of genus at least 4, we confirm a conjecture of Farb that . More generally, we show that any injection of a finite index subgroup of into the Torelli group of is induced by a homeomorphism. In particular, this proves that is co-Hopfian and is characteristic in . Further, we recover the result of Farb and Ivanov that any injection of a finite index subgroup of into is induced by a homeomorphism. Our method is to reformulate these group theoretic statements in terms of maps of curve complexes.
Citation
Tara E Brendle. Dan Margalit. "Commensurations of the Johnson kernel." Geom. Topol. 8 (3) 1361 - 1384, 2004. https://doi.org/10.2140/gt.2004.8.1361
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