一个由区间的C^1同态生成的无忠实作用的局部可指示群
A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval
摘要：
根据Thurston稳定性定理，闭区间的每个C^1同构群都是局部可指示的（即，每个子组通过Z生成子组因子）。我们证明了，即使对于有限生成群，这种说法的逆是不正确的。更精确地说，我们证明了F_2和Z^2的半直积虽然是局部可指示的，但不嵌入Diff_+^1（] 0，1 [）中. (Here F_2是SL（2，Z）的任意自由子群，它在Z^2上的作用是投射作用。进一步证明了对SL（2，Z）的每个非可解子群G，G与Z^2的半直积不嵌入Diff^1_+（S^1）.
英文摘要：
According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct product between F_2 an Z^2, although locally indicable, does not embed into Diff_+^1 (]0,1[). (Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is the projective one.) Moreover, we show that for every non-solvable subgroup G of SL(2,Z), the semi-direct product between G and Z^2 does not embed into Diff^1_+(S^1).
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