Quasisymmetric Nonparametrization and Spaces Associated with the Whitehead Continuum

@inproceedings{Heinonen2009QuasisymmetricNA,
  title={Quasisymmetric Nonparametrization and Spaces Associated with the Whitehead Continuum},
  author={J. Heinonen and J Wu},
  year={2009}
}
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

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 41 references

Conformal invariants and function-theoretic null-sets

  • L Ahlfors, A Beurling
  • Acta Math. 83
  • 1950
Highly Influential
15 Excerpts

Strange actions of groups on spheres

  • M H Freedman, R Skora
  • J. Differential Geom. 25
  • 1987
Highly Influential
6 Excerpts

Thirty-three yes or no questions about mappings

  • J Heinonen, S Semmes
  • measures, and metrics, Geom. Dyn., electronic 1
  • 1997
Highly Influential
8 Excerpts

The topology of 4-manifolds

  • R C Kirby
  • volume 1374 of Lecture Notes in Mathematics…
  • 1989
Highly Influential
6 Excerpts

Decompositions of manifolds

  • R J Daverman
  • volume 124 of Pure and Applied Mathematics…
  • 1986
Highly Influential
5 Excerpts

Introduction to piecewise-linear topology

  • C P Rourke, B J Sanderson
  • Springer Study Edition, Springer-Verlag, Berlin
  • 1982
Highly Influential
4 Excerpts

Quasisymmetric embeddings of metric spaces

  • P Tukia, J Väisälä
  • Ann. Acad. Sci. Fenn. Ser. A I Math. 5
  • 1980
Highly Influential
5 Excerpts

Geometric topology in dimensions 2 and 3

  • E E Moise
  • Springer-Verlag, New York
  • 1977
Highly Influential
3 Excerpts

Topological and metric properties of quasiregular mappings

  • O Martio, S Rickman, J Väisälä
  • Ann. Acad. Sci. Fenn. Ser. A I
  • 1971
Highly Influential
4 Excerpts

The cartesian product of a certain nonmanifold and a line is E4

  • R H Bing
  • Ann. of Math. (2) 70
  • 1959
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…