Volume 8, issue 3 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 2487–3110
Issue 4, 1865–2486
Issue 3, 1245–1863
Issue 2, 617–1244
Issue 1, 1–616

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
G&T Publications
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Commensurations of the Johnson kernel

Tara E Brendle and Dan Margalit

Geometry & Topology 8 (2004) 1361–1384

arXiv: math.GT/0404445


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)Mod(S). More generally, we show that any injection of a finite index subgroup of K into the Torelli group of S is induced by a homeomorphism. In particular, this proves that K is co-Hopfian and is characteristic in . Further, we recover the result of Farb and Ivanov that any injection of a finite index subgroup of into is induced by a homeomorphism. Our method is to reformulate these group theoretic statements in terms of maps of curve complexes.

Torelli group, mapping class group, Dehn twist
Mathematical Subject Classification 2000
Primary: 57S05
Secondary: 20F38, 20F36
Forward citations
Received: 15 June 2004
Revised: 25 October 2004
Accepted: 25 October 2004
Published: 25 October 2004
Proposed: Walter Neumann
Seconded: Shigeyuki Morita, Joan Birman
Tara E Brendle
Department of Mathematics
Cornell University
310 Malott Hall
New York 14853
Dan Margalit
Department of Mathematics
University of Utah
155 South 1440 East
Salt Lake City
Utah 84112