A finitely generated, locally indicable group with no faithful action by C-1 diffeomorphisms of the interval

作者：Navas Andres^*

来源：Geometry and Topology, 2010, 14(1): 573-584.

DOI：10.2140/gt.2010.14.573

According to Thurston's stability theorem, every group of C-1 diffeomorphisms of the closed interval is locally indicable (that is, 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 F-2 x 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 linear one.) Moreover, we show that for every non-solvable subgroup G of SL(2, Z), the group G x Z(2) does not embed into Diff(+)(1)(S-1).

• 出版日期2010