Uncountably many inequivalent analytic actions of a compact group on $R\sp{n}$

Uncountably Many Inequivalent Analytic Actions of a Compact Group on A"

According to a result of one of the authors [7] there are at most a countable number of inequivalent differentiable actions of a compact Lie group on a compact differentiable manifold. The results above show that both the compactness of the manifold and the differentiability of the action are necessary assumptions. In the course of our proof we also prove the following theorem, which is an elem...

Inequivalent, bordant group actions on a surface

We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with (g) orientation-preserving for all g e G. In addition we will consider only effective ( is injective) free actions. Free means that (g) is fixed-point-free for all geG, g 4= 1. This paper addresses the classification of such actions. Given an action of G on F, as above, new actions c...

Uncountably Many Inequivalent Lipschitz Homogeneous Cantor Sets in Ir

Lie group actions on compact

Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.

Spaces of Uncountably Many Dimensions*

Riemann in his Habilitations Schrift of 1854 suggested the notion of ^-dimensional space (where n is a natural number) as an extension of the notion of three-dimensional euclidean space. Hubert extended the notion still further by defining a space of a countably infinite number of dimensions. Fréchetf in 1908 defined two other spaces of countably many dimensions, which he called D„ and J3W. Tyc...