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

@inproceedings{Edelsbrunner2011AlexanderDF,
  title={Alexander duality for functions: the persistent behavior of land and water and shore},
  author={Herbert Edelsbrunner and Michael Kerber},
  booktitle={SoCG '12},
  year={2011}
}
  • Herbert Edelsbrunner, Michael Kerber
  • Published in SoCG '12 2011
  • Mathematics, Computer Science
  • 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: Sspacen+1 -> [0,1] and a decomposition Sspacen+1 = Uspace ∪ Vspace into two (n+1)-manifolds with common boundary Mspace, we prove elementary relationships between the persistence diagrams of f restricted to Uspace, to Vspace, and to Mspace. 

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