Geometry & Topology

Addendum to: Commensurations of the Johnson kernel

Tara E Brendle and Dan Margalit

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Let K(S) be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. In our earlier paper, we showed that Comm(K(S))Aut(K(S))Mod(S) when S is a closed, connected, orientable surface of genus g4. By modifying our original proof, we show that the same result holds for g3, thus confirming Farb’s conjecture in all cases (the statement is not true for g2).

Article information

Geom. Topol., Volume 12, Number 1 (2008), 97-101.

Received: 13 September 2007
Accepted: 12 October 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F36: Braid groups; Artin groups

Johnson kernel Torelli group automorphisms abstract commensurator


Brendle, Tara E; Margalit, Dan. Addendum to: Commensurations of the Johnson kernel. Geom. Topol. 12 (2008), no. 1, 97--101. doi:10.2140/gt.2008.12.97.

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  • T E Brendle, D Margalit, Commensurations of the Johnson kernel, Geom. Topol. 8 (2004) 1361–1384
  • B Farb, Automorphisms of the Torelli group, AMS sectional meeting, Ann Arbor, Michigan, March 1 (2002)
  • B Farb, N V Ivanov, The Torelli geometry and its applications: research announcement, Math. Res. Lett. 12 (2005) 293–301
  • E Irmak, Superinjective simplicial maps of complexes of curves and injective homomorphisms of subgroups of mapping class groups, Topology 43 (2004) 513–541
  • J D McCarthy, W R Vautaw, Automorphisms of Torelli groups
  • G Mess, The Torelli groups for genus $2$ and $3$ surfaces, Topology 31 (1992) 775–790