Alexander duality for functions: The persistent behavior of land and water and shore

conference paper Alexander duality for functions: The persistent behavior of land and water and shore published yes Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Michael Kerber author 36E4574A-F248-11E8-B48F-1D18A9856A870000-0002-8030-9299 HeEd department SCG: Symposium on Computational Geometry 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. ACM2012Chapel Hill, NC, USA eng Proceedings of the twenty-eighth annual symposium on Computational geometry 1109.505210.1145/2261250.2261287 249 - 258 H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258. Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258. Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–58, doi:<a href="https://doi.org/10.1145/2261250.2261287">10.1145/2261250.2261287</a>. Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 249–58. ACM, 2012. <a href="https://doi.org/10.1145/2261250.2261287">https://doi.org/10.1145/2261250.2261287</a>. Edelsbrunner, H., & Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 249–258). Chapel Hill, NC, USA: ACM. <a href="https://doi.org/10.1145/2261250.2261287">https://doi.org/10.1145/2261250.2261287</a> Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:249-258. doi:<a href="https://doi.org/10.1145/2261250.2261287">10.1145/2261250.2261287</a> H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 249–258. 31332018-12-11T12:01:35Z2025-06-11T08:10:04Z