Groups of homeomorphisms of one-manifolds, III: Nilpotent subgroups
نویسندگان
چکیده
This self-contained paper is part of a series [FF1, FF2] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. Plante-Thurston proved that every nilpotent subgroup of Diff(S) is abelian. One of our main results is a sharp converse: Diff(S) contains every finitely-generated, torsion-free nilpotent group.
منابع مشابه
Ergodic Theory and Dynamical Systems
Let M be a connected 1-manifold, and let G be a finitely-generated nilpotent group of homeomorphisms of M . Our main result is that one can find a collection {Ii, j , Mi, j } of open disjoint intervals with dense union in M , such that the intervals are permuted by the action of G, and the restriction of the action to any Ii, j is trivial, while the restriction of the action to any Mi, j is min...
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تاریخ انتشار 2001