Contraction of areas vs. topology of mappings
Differential Geometry
2013-05-31 v3 Geometric Topology
Abstract
We construct homotopically non-trivial maps from the unit m-sphere to the unit (m-1)-sphere with arbitrarily small k-dilation for each k greater than (m + 1)/2. We prove that homotopically non-trivial maps from the unit m-sphere to the unit (m-1)-sphere cannot have arbitrarily small k-dilation for k less than or equal to (m + 1)/2.
Keywords
Cite
@article{arxiv.1211.1057,
title = {Contraction of areas vs. topology of mappings},
author = {Larry Guth},
journal= {arXiv preprint arXiv:1211.1057},
year = {2013}
}
Comments
82 pages. Typos corrected. Reference added to a recent paper of Wenger and Young. Accepted for publication in Geometric and Functional Analysis