The decomposition space R3/Wh associated with the Whitehead continuum Wh is not a manifold, but the product (R3/Wh) × Rm is homeomorphic to R3+m for any m≥1 (known since the 1960's). We study the quasisymmetric structure on.(R3/Wh) × Rm and show that the space (R3/Wh) × Rm may be equipped with a metric resembling R3+m geometrically and measure theoretically-it is linearly locally contractible and Ahlfors (3+m)-regular-nevertheless the resulting space does not admit a quasisymmetric parametrization by R3+m.
ASJC Scopus subject areas
- Geometry and Topology