Alexander duality for functions: The persistent behavior of land and water and shore Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Kerber, Michael ; https://orcid.org/0000-0002-8030-9299 This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. ACM 2012 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/3133 Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:249-258. doi:<a href="https://doi.org/10.1145/2261250.2261287">10.1145/2261250.2261287</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1145/2261250.2261287 info:eu-repo/semantics/altIdentifier/arxiv/1109.5052 info:eu-repo/semantics/openAccess