On the linearity problem for mapping class groups
On the linearity problem for mapping class groups
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关于映射类群的线性问题
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Hessam Hamidi
中科院分区：
文献类型：
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作者：
Tara E. Brendle;Hessam Hamidi
Formanek和Procesi证明了Aut（Fn）对n 3不是线性的.他们的技术是构造一种特殊形式的非线性群，我们称之为FP-群，然后嵌入一种特殊类型的自同构群，我们称之为毒群i n Aut（F n），他们从其中构建FP-群。我们首先证明了毒药组不能嵌入到某些映射类组。然后，我们表明，没有任何形式的FP-组可以嵌入到映射类组。因此，Formanek和Procesi的方法在映射类群的情况下失败，提供了强有力的证据表明映射类群实际上可能是线性的。AMS分类57 M07，20 F65; 57 N 05，20 F34
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 ,i n Aut( F n), from which they build an FP-group. We rst 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. AMS Classication 57M07,20F65; 57N05,20F34