Homotopically non-trivial maps with small k-dilation

Details Homotopically non-trivial maps with small k-dilation Homotopically non-trivial maps with small k-dilation

2007-09-09

arxiv.org/abs/0709.1241v1

Mathematics

Differential Geometry

7 pages

Scientific paper

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.

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