Abstract
We construct homotopically non-trivial maps from S m to S m−1 with arbitrarily small k-dilation for each k > (m + 1)/2. We prove that homotopically non-trivial maps from S m to S m−1 cannot have arbitrarily small k-dilation for k ≤ (m + 1)/2.
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Guth, L. Contraction of Areas vs. Topology of Mappings. Geom. Funct. Anal. 23, 1804–1902 (2013). https://doi.org/10.1007/s00039-013-0246-3
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DOI: https://doi.org/10.1007/s00039-013-0246-3