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Groups of homeomorphisms of one-manifolds III: nilpotent subgroups

Published online by Cambridge University Press:  23 September 2003

BENSON FARB  and
JOHN FRANKS
BENSON FARB
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA (e-mail: [email protected])
JOHN FRANKS
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA (e-mail: [email protected])
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Abstract

This self-contained paper is part of a series (Groups of homeomorphisms of one-manifolds I: actions of nonlinear groups. Preprint, 2001; Group actions on one-manifolds II: extensions of Hölder's Theorem. To appear in Trans. Amer. Math. Soc.) seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. Plante and Thurston proved that every nilpotent subgroup of Diff2(S1) is abelian. One of our main results is a sharp converse: Diff1(S1) contains every finitely generated, torsion-free nilpotent group.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 5 , October 2003 , pp. 1467 - 1484
Copyright
2003 Cambridge University Press

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