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On the linearity problem for mapping class groups

Tara E Brendle and Hessam Hamidi-Tehrani

Algebraic & Geometric Topology 1 (2001) 445–468

arXiv: math.GT/0103148


Formanek and Procesi have demonstrated that Aut(Fn) is not linear for n 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(Fn), 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.

mapping class group, linearity, poison group
Mathematical Subject Classification 2000
Primary: 57M07, 20F65
Secondary: 57N05, 20F34
Forward citations
Received: 24 March 2001
Revised: 17 August 2001
Accepted: 17 August 2001
Published: 23 August 2001
Tara E Brendle
Columbia University
Department of Mathematics
New York NY 10027
Hessam Hamidi-Tehrani
B.C.C. of the City University of New York
Department of Mathematics and Computer Science
Bronx NY 10453