Extending functions from a neighborhood of the sphere to the ball

Valentin Seigneur

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arXiv · 1805.06840

Extending functions from a neighborhood of the sphere to the ball

Valentin Seigneur

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Abstract

In this article, we are interested in the problem of extending the germ of a smooth function $\tilde{f}$ defined along the standard sphere of dimension $n$ to a function defined on the ball which has no critical points. The article gives a necessary condition using the Morse chain complex associated to the function $f$, restriction of $\tilde{f}$ to the sphere $\mathbb{S}^n$, which is assumed to be a Morse function.

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BibTeX RIS

Valentin Seigneur. 2018-05-17. Extending functions from a neighborhood of the sphere to the ball. https://arxiv.org/abs/1805.06840

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