The fundamental group of a compact metric space

Quantum isometry group of a compact metric space

We give a definition of isometric action of a compact quantum group on a compact metric space, generalizing the definition given by Banica for finite metric spaces, and prove the existence of the universal object in the category of compact quantum groups acting isometrically on a given compact metric space.

THE FUNDAMENTAL GROUP OF A p-COMPACT GROUP

The notion of p-compact group [10] is a homotopy theoretic version of the geometric or analytic notion of compact Lie group, although the homotopy theory differs from the geometry is that there are parallel theories of p-compact groups, one for each prime number p. A key feature of the theory of compact Lie groups is the relationship between centers and fundamental groups; these play off agains...

Tchebycheff Approximation in a Compact Metric Space

Pdmi Preprint | 05/2002 on the Fundamental Group of a Compact Space without Conjugate Points

In 1986, C. Croke and V. Schroeder proved that the fundamental group ? of a compact analytic Riemannian manifold without conjugate points possesses the following property: every abelian subgroup ? 0 of ? is straight, that is, word metrics of ? and ? 0 are Lipschitz equivalent on ? 0. In this paper we prove that the same property holds for the fundamental group of any compact length space withou...

The Group of Isometries of a Locally Compact Metric Space with One End

In this note we study the dynamics of the natural evaluation action of the group of isometries G of a locally compact metric space (X, d) with one end. Using the notion of pseudocomponents introduced by S. Gao and A. S. Kechris we show that X has only finitely many pseudo-components exactly one of which is not compact andG acts properly on this pseudo-component. The complement of the non-compac...