Mazurkiewicz manifolds and homogeneity

Mazurkiewicz Manifolds and Homogeneity

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an Fσ-subset of a “smaller” dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces. The classical Hurewicz-Menger-Tumarkin theorem in dimension theory says that connected topological n-manifolds (with or without boundary) are Cantor manifo...

Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces

Generalizations of Mazurkiewicz Traces

This Master's Thesis represents the nal part of my computer science study in Leiden. I would like to thank my supervisor Jetty Kleijn for her support.

On Different Notions of Homogeneity for Cr-manifolds

We show that various notions of local homogeneity for CR-manifolds are equivalent. In particular, if germs at any two points of a CR-manifold are CR-equivalent, there exists a transitive local Lie group action by CR-automorphisms near every point.

The curvature homogeneity bound for four-dimensional Lorentzian manifolds

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. Our results imply that the Singer index for four-dimensional Lorentzian manifolds is greater or equal to 2. PACS numbers: 04.20, 02.40 AMS classificat...