On the linearity problem for mapping class groups

Formanek and Procesi have demonstrated that $Aut (F_{n})$ is not linear for $n \geq 3$ . Their technique is to construct nonlinear groups of a special form, which we call FP-groups, and then to embed a special type of automorphism group, which we call a poison group, in $Aut (F_{n})$ , from which they build an FP-group. We first prove that poison groups cannot be embedded in certain mapping class groups. We then show that no FP-groups of any form can be embedded in mapping class groups. Thus the methods of Formanek and Procesi fail in the case of mapping class groups, providing strong evidence that mapping class groups may in fact be linear.

Keywords

mapping class group, linearity, poison group

Mathematical Subject Classification 2000

Primary: 57M07, 20F65

Secondary: 57N05, 20F34

References

Forward citations

Publication

Received: 24 March 2001

Revised: 17 August 2001

Accepted: 17 August 2001

Published: 23 August 2001

Authors

Tara E Brendle
Columbia University Department of Mathematics New York NY 10027 USA

Hessam Hamidi-Tehrani
B.C.C. of the City University of New York Department of Mathematics and Computer Science Bronx NY 10453 USA

Volume 1, issue 1 (2001)

Tara E Brendle and Hessam Hamidi-Tehrani