2011/09/23 by Herbert Edelsbrunner, Edelsbrunner, Herbert, Michael Kerber +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #cs.CG #math.AT #math.GT
paper · pdf · doi:10.48550/arxiv.1109.5052
Keywords: Algebraic topology, homology, Alexander duality, Mayer-Vietoris sequences, persistent homology, point calculus
arxiv created 2011/09/23 · arxiv updated 2011/09/26
This note contributes to the point calculus of persistent homology by extending Alexander duality to real-valued functions. Given a perfect Morse function f: Sn+1 → [0,1] and a decomposition Sn+1 = U ∪ V such that M = \U ∩ V is an n-manifold, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M.