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arXiv · 1211.1057

Contraction of areas vs. topology of mappings

Larry Guth
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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.

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Larry Guth. 2013-05-29. Contraction of areas vs. topology of mappings. https://arxiv.org/abs/1211.1057

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