faithful action by C 1 diffeomorphisms of the interval
نویسنده
چکیده
According to Thurston’s stability theorem, every group of C diffeomorphisms of the closed interval is locally indicable (i.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 group F2 ⋉ Z , although locally indicable, does not embed into Diff1+(]0, 1[). (Here F2 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 group G⋉ Z does not embed into Diff1+(S ). MSC-class: 20B27, 37C85, 37E05.
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تاریخ انتشار 2009