Quasisymmetric nonparametrization and spaces associated with the Whitehead continuum

Juha Heinonen, Jang Mei Wu

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)773-798
Number of pages26
JournalGeometry and Topology
Volume14
Issue number2
DOIs
StatePublished - 2010

ASJC Scopus subject areas

  • Geometry and Topology

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