Extending Persistence Using Poincaré and Lefschetz Duality

Learn how to extend persistence by using Poincaré and Lefschetz Duality in this 13-minute tutorial from the Applied Algebraic Topology Network. Discover why traditional persistence computation through sublevel sets of a function can miss crucial shape features, and explore how duality principles can help pair all critical points of height functions defined on codimension 1 submanifolds of Euclidean space. Follow along with practical examples and gain valuable insights on interpreting the four persistence diagrams produced through extended persistence, enhancing your ability to recognize and analyze topological features.