This work 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.

Joint work with Herbert Edelsbrunner