English

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.

Keywords

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

R2 v1 2026-06-21T09:15:21.615Z