Contraction of Areas vs. Topology of Mappings |
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Authors: | Larry Guth |
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Institution: | 1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA
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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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