Quantitative nullhomotopy and the Hopf Invariant

Luis Kumanduri

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arXiv · 2106.01456

Quantitative nullhomotopy and the Hopf Invariant

Luis Kumanduri

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Abstract

Let $G: S^{4n-1} \rightarrow S^{2n}$ be a map with nonzero Hopf Invariant. Using the generalized Hopf invariant introduced by Haj\l{}asz, Schikorra and Tyson, we show that any null-homotopy $F: B^{4n} \rightarrow B^{2n+1}$ of $G$ with small $(2n+1)$-dilation must have large $(2n)$-dilation. Conversely, we show that these results are sharp by constructing smooth null-homotopies with arbitrarily small $(2n+1)$-dilation.

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BibTeX RIS

Luis Kumanduri. 2021-06-02. Quantitative nullhomotopy and the Hopf Invariant. https://arxiv.org/abs/2106.01456

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