@inproceedings{3133,
abstract = {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. },
author = {Edelsbrunner, Herbert and Kerber, Michael},
booktitle = {Proceedings of the twenty-eighth annual symposium on Computational geometry },
location = {Chapel Hill, NC, USA},
pages = {249 -- 258},
publisher = {ACM},
title = {{Alexander duality for functions: The persistent behavior of land and water and shore}},
doi = {10.1145/2261250.2261287},
year = {2012},
}