Algebraic and Geometric Topology 1 (2001), paper no. 23, pages 445-468.

On the linearity problem for mapping class groups

Tara E. Brendle, Hessam Hamidi-Tehrani

Abstract. Formanek and Procesi have demonstrated that Aut(F_n) is not linear for n >2. 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

AMS subject classification. Primary: 57M07,20F65. Secondary: 57N05,20F34.

DOI: 10.2140/agt.2001.1.445

E-print: arXiv:math.GT/0103148

Submitted: 24 March 2001. (Revised: 17 August 2001.) Accepted: 17 August 2001. Published: 23 August 2001.

Notes on file formats

Tara E. Brendle, Hessam Hamidi-Tehrani
Columbia University
Department of Mathematics
New York, NY 10027, USA

B.C.C. of the City University of New York
Department of Mathematics and Computer Science
Bronx, NY 10453, USA

Email: tbrendle@math.columbia.edu, hessam@math.columbia.edu

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