Generalized Morse theory for tubular neighborhoods

Antoine Commaret

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arXiv · 2401.04034

Generalized Morse theory for tubular neighborhoods

Antoine Commaret

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Abstract

We define a notion of Morse function and establish Morse theory-like theorems over offsets of any compact set in a Euclidean space at regular values of their distance function. Using non-smooth analysis and tools from geometric measure theory, we prove that the homotopy type of the sublevels sets of these Morse functions changes at a critical value by gluing exactly one cell around each critical point.

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BibTeX RIS

Antoine Commaret. 2024-01-08. Generalized Morse theory for tubular neighborhoods. https://arxiv.org/abs/2401.04034

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