Volume 12, issue 1 (2008)

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Addendum to: Commensurations of the Johnson kernel

Tara E Brendle and Dan Margalit

Geometry & Topology 12 (2008) 97–101
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 4. By modifying our original proof, we show that the same result holds for g 3, thus confirming Farb’s conjecture in all cases (the statement is not true for g 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