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arXiv · 1109.5052

Alexander Duality for Functions: the Persistent Behavior of Land and Water and Shore

Herbert Edelsbrunner·Michael Kerber
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Abstract

This note contributes to the point calculus of persistent homology by extending Alexander duality to real-valued functions. Given a perfect Morse function $f: S^{n+1} \to [0,1]$ and a decomposition $S^{n+1} = U \cup V$ such that $M = \U \cap V$ is an $n$-manifold, we prove elementary relationships between the persistence diagrams of $f$ restricted to $U$, to $V$, and to $M$.

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BibTeXRIS

Herbert Edelsbrunner, Michael Kerber. 2011-09-23. Alexander Duality for Functions: the Persistent Behavior of Land and Water and Shore. https://arxiv.org/abs/1109.5052

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