2,057 research outputs found
Structure theorems for subgroups of homeomorphisms groups
In this partly expository paper, we study the set A of groups of
orientation-preserving homeomorphisms of the circle S^1 which do not admit
non-abelian free subgroups. We use classical results about homeomorphisms of
the circle and elementary dynamical methods to derive various new and old
results about the groups in A. Of the known results, we include some results
from a family of results of Beklaryan and Malyutin, and we also give a new
proof of a theorem of Margulis. Our primary new results include a detailed
classification of the solvable subgroups of R. Thompson's group T .Comment: 31 pages, 3 figures; final version, to appear in "International
Journal of Algebra and Computation
Geometry and topology of complex hyperbolic and CR-manifolds
We study geometry, topology and deformation spaces of noncompact complex
hyperbolic manifolds (geometrically finite, with variable negative curvature),
whose properties make them surprisingly different from real hyperbolic
manifolds with constant negative curvature. This study uses an interaction
between K\"ahler geometry of the complex hyperbolic space and the contact
structure at its infinity (the one-point compactification of the Heisenberg
group), in particular an established structural theorem for discrete group
actions on nilpotent Lie groups
Actions of automorphism groups of free groups on homology spheres and acyclic manifolds
For n at least 3, let SAut(F_n) denote the unique subgroup of index two in
the automorphism group of a free group. The standard linear action of SL(n,Z)
on R^n induces non-trivial actions of SAut(F_n) on R^n and on S^{n-1}. We prove
that SAut(F_n) admits no non-trivial actions by homeomorphisms on acyclic
manifolds or spheres of smaller dimension. Indeed, SAut(F_n) cannot act
non-trivially on any generalized Z_2-homology sphere of dimension less than
n-1, nor on any Z_2-acyclic Z_2-homology manifold of dimension less than n. It
follows that SL(n,Z) cannot act non-trivially on such spaces either. When n is
even, we obtain similar results with Z_3 coefficients.Comment: Typos corrected, reference and thanks added. Final version, to appear
in Commetarii. Math. Hel
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