Geometry and quasisymmetric parametrization of Semmes spaces

@article{Pankka2011GeometryAQ,
  title={Geometry and quasisymmetric parametrization of Semmes spaces},
  author={Pekka Pankka and Jang-Mei Gloria Wu},
  journal={Revista Matematica Iberoamericana},
  year={2011},
  volume={30},
  pages={893-960}
}
  • Pekka Pankka, J. Wu
  • Published 9 November 2011
  • Mathematics
  • Revista Matematica Iberoamericana
We consider decomposition spaces R/G that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on R/G constructed via modular embeddings of R/G into Euclidean spaces promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R/G×R by R for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, to the defining sequences for R/G. We… 

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