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- W2963472625 abstract "Abstract We prove the following dichotomy: if $n=2,3$ and $fin C^1(mathbb{S}^{n+1},mathbb{S}^n)$ is not homotopic to a constant map, then there is an open set $Omega subset mathbb{S}^{n+1}$ such that $operatorname{rank} df=n$ on $Omega $ and $f(Omega )$ is dense in $mathbb{S}^n$, while for any $ngeq 4$, there is a map $fin C^1(mathbb{S}^{n+1},mathbb{S}^n)$ that is not homotopic to a constant map and such that $operatorname{rank} df<n$ everywhere. The result in the case $ngeq 4$ answers a question of Larry Guth." @default.
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- W2963472625 date "2018-08-31" @default.
- W2963472625 modified "2023-10-18" @default.
- W2963472625 title "Topologically Nontrivial Counterexamples to Sard’s Theorem" @default.
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- W2963472625 doi "https://doi.org/10.1093/imrn/rny179" @default.
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