# 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}
}
• 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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