Topologically nontrivial counterexamples to Sard's theorem
| Autor: | Goldstein, Paweł, Hajłasz, Piotr, Pankka, Pekka |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove the following dichotomy: if $n=2,3$ and $f\in C^1(\mathbb{S}^{n+1},\mathbb{S}^n)$ is not homotopic to a constant map, then there is an open set $\Omega\subset\mathbb{S}^{n+1}$ such that $\mathrm{rank}\, df=n$ on $\Omega$ and $f(\Omega)$ is dense in $\mathbb{S}^n$, while for any $n\geq 4$, there is a map $f\in C^1(\mathbb{S}^{n+1},\mathbb{S}^n)$ that is not homotopic to a constant map and such that $\mathrm{rank}\, df |
| Databáze: | arXiv |
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