Quasisymmetric Nonparametrization and Spaces Associated with the Whitehead Continuum

  title={Quasisymmetric Nonparametrization and Spaces Associated with the Whitehead Continuum},
  author={J. Heinonen and J Wu},
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… CONTINUE READING

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