Commensurations of the Johnson kernel

Brendle, T.E. and Margalit, D. (2004) Commensurations of the Johnson kernel. Geometry and Topology, 8, pp. 1361-1384. (doi: 10.2140/gt.2004.8.1361)

Abstract

Let K be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. Assuming that S is a closed, orientable surface of genus at least 4, we confirm a conjecture of Farb that Comm(K), Aut(K) and Mod(S) are all isomorphic. More generally, we show that any injection of a finite index subgroup of K into the Torelli group I of S is induced by a homeomorphism. In particular, this proves that K is co-Hopfian and is characteristic in I. Further, we recover the result of Farb and Ivanov that any injection of a finite index subgroup of I into I is induced by a homeomorphism. Our method is to reformulate these group theoretic statements in terms of maps of curve complexes.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Brendle, Professor Tara
• Authors: Brendle, T.E., and Margalit, D.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Geometry and Topology
• ISSN: 1465-3060
• ISSN (Online): 1364-0380

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