Wrinkled Embeddings

Details Wrinkled Embeddings Wrinkled Embeddings

2011-08-05

arxiv.org/abs/1108.1265v1

Contemporary Mathematics, Volume 498, 2009, 207-232

Mathematics

Geometric Topology

38 pages, 14 figures

Scientific paper

A {\it wrinkled embedding} $f:V^n\to W^m$ is a topological embedding which is a smooth embedding everywhere on $V$ except a set of $(n-1)$-dimensional spheres, where $f$ has cuspidal corners. In this paper we prove that any rotation of the tangent plane field $TV\subset TW$ of a {\it smoothly embedded} submanifold $V\subset W$ can be approximated by a homotopy of {\it wrinkled embeddings} $V\to W$.

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