Exceptional minimal sets of C1+α-group actions on the circle

Hamiltonian Circle Actions with Minimal Fixed Sets

Consider an effective Hamiltonian circle action on a compact symplectic 2n-dimensional manifold (M, ω). Assume that the fixed set M 1 is minimal, in two senses: it has exactly two components, X and Y , and dim(X) + dim(Y ) = dim(M)− 2. We prove that the integral cohomology ring and Chern classes of M are isomorphic to either those of CP or to those of e G2(R), where e G2(R) denotes the Grassman...

Minimal Group Actions on Dendrites

Minimal group actions on dendrites appear naturally in the study of 3-dimensional hyperbolic geometry. In this paper, it is shown that if a group G acts on a nondegenerate dendrite X minimally, then X admits no G-invariant measure. In particular, G cannot be amenable.

Group Actions on Amorphous Sets

Rigidity and flexibility of group actions on the circle

3 An introduction to rigidity 7 3.1 Local rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Full rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Strong (Mostow) Rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 The Zimmer program . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Rotation spectra and exotic group actions on the circle

We develop a general framework for producing uncountable families of exotic actions of certain classically studied groups on the circle. We show that if G is a closed surface group then there are connected components of the nonlinear representation variety HompG,Homeo`pS 1qq which contain uncountably many semi-conjugacy classes of G–actions, thus complementing a result of K. Mann. We also exhib...