Addendum to: Commensurations of the Johnson kernel

Brendle, Tara E¹ ; Margalit, Dan²

¹ Department of Mathematics, Louisiana State University, Baton Rouge LA 70803-4918, USA
² Department of Mathematics, University of Utah, 155 S 1400 East, Salt Lake City UT 84112, USA

Geometry & topology, Tome 12 (2008) no. 1, pp. 97-101.

Résumé

Let $\mathcal{K}\left(S\right)$ be the subgroup of the extended mapping class group, $Mod\left(S\right)$, generated by Dehn twists about separating curves. In our earlier paper, we showed that $Comm\left(\mathcal{K}\left(S\right)\right)\cong Aut\left(\mathcal{K}\left(S\right)\right)\cong Mod\left(S\right)$ when $S$ is a closed, connected, orientable surface of genus $g\ge 4$. By modifying our original proof, we show that the same result holds for $g\ge 3$, thus confirming Farb’s conjecture in all cases (the statement is not true for $g\le 2$).

Détail

DOI : 10.2140/gt.2008.12.97

Keywords: Johnson kernel, Torelli group, automorphisms, abstract commensurator

Bibliographie

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