Merge trees and sublevelset persistent homology

Title: Merge trees and sublevelset persistent homology Abstract: In this tutorial we give an introduction to merge trees and sublevelset persistent homology. Merge trees and 0-dimensional persistent homology contain similar information: the heights of the local minima, and of the index 1 saddle points that merge connected components. By contrast, 1-dimensional persistent homology also measures the heights of the index 1 saddle points that create loops, along with some of the heights of index 2 critical points.