Homotopically non-trivial maps with small k-dilation
Differential Geometry
2007-09-11 v1
Abstract
We construct homotopically non-trivial maps from S^m to S^n with arbitrarily small 3-dilation for certain pairs (m,n). The simplest example is m=4, n=3. Other examples include arbitrarily large values of m and n. We show that a homotopy class in pi_7(S^4) can be represented by maps with arbitrarily small 4-dilation if and only if the class is torsion.
Cite
@article{arxiv.0709.1241,
title = {Homotopically non-trivial maps with small k-dilation},
author = {Larry Guth},
journal= {arXiv preprint arXiv:0709.1241},
year = {2007}
}
Comments
7 pages