Geometry & Topology
- Geom. Topol.
- Volume 8, Number 3 (2004), 1361-1384.
Commensurations of the Johnson kernel
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.
Geom. Topol., Volume 8, Number 3 (2004), 1361-1384.
Received: 15 June 2004
Revised: 25 October 2004
Accepted: 25 October 2004
First available in Project Euclid: 21 December 2017
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Brendle, Tara E; Margalit, Dan. Commensurations of the Johnson kernel. Geom. Topol. 8 (2004), no. 3, 1361--1384. doi:10.2140/gt.2004.8.1361. https://projecteuclid.org/euclid.gt/1513883470