Search results for "decomposition space"
showing 2 items of 2 documents
Quasiregular ellipticity of open and generalized manifolds
2014
We study the existence of geometrically controlled branched covering maps from \(\mathbb R^3\) to open \(3\)-manifolds or to decomposition spaces \(\mathbb {S}^3/G\), and from \(\mathbb {S}^3/G\) to \(\mathbb {S}^3\).
Geometry and quasisymmetric parametrization of Semmes spaces
2011
We consider decomposition spaces R 3 /G that are manifold factors and admit defining sequences consisting of cubes-with-handles of finite type. Metrics on R 3 /G constructed via modular embeddings of R 3 /G into a Euclidean space promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R 3 /G×R m by R 3+m for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, on the defining sequences for R 3 /G. We give a necessary condition and a sufficient condition for the existence of such a parametrization. The necessary condition answers negatively a question of Heinone…