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


Author(s): Edelsbrunner, Herbert; Kerber, Michael
Title: Alexander duality for functions: The persistent behavior of land and water and shore
Affiliation IST Austria
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.
Keywords: persistent homology; Homology; Algebraic topology; Alexander duality; Mayer-Vietoris sequences; Point calculus
Conference Title: SCG: Symposium on Computational Geometry
Conference Dates: June 17-20, 2012
Conference Location: Chapel Hill, NC, USA
Publisher: ACM  
Location: New York, NY, USA
Date Published: 2012-06-20
Start Page: 249
End Page: 258
Sponsor: his research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624, the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.
URL:
DOI: 10.1145/2261250.2261287
Notes: The authors thank an anonymous referee for suggesting the simplified proof of the Contravariant PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and Amit Patel for helpful discussions.
Open access: yes (repository)
IST Austria Authors
  1. Michael Kerber
    21 Kerber
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