Addendum to: Commensurations of the Johnson kernel

Brendle, Tara E; Margalit, Dan

doi:10.2140/gt.2008.12.97

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Addendum to: Commensurations of the Johnson kernel

Tara E Brendle and Dan Margalit

Geometry & Topology 12 (2008) 97–101

DOI: 10.2140/gt.2008.12.97

Abstract

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 $g \geq 4$ . By modifying our original proof, we show that the same result holds for $g \geq 3$ , thus confirming Farb’s conjecture in all cases (the statement is not true for $g \leq 2$ ).

Keywords

Johnson kernel, Torelli group, automorphisms, abstract commensurator

Mathematical Subject Classification 2000

Primary: 20F36

References

Publication

Received: 13 September 2007

Accepted: 12 October 2007

Published: 8 February 2008

Proposed: Walter Neumann

Seconded: Joan Birman, Shigeyuki Morita

Authors

Tara E Brendle
Department of Mathematics Louisiana State University Baton Rouge LA 70803-4918 USA

Dan Margalit
Department of Mathematics University of Utah 155 S 1400 East Salt Lake City UT 84112 USA

Volume 12, issue 1 (2008)