Topological Signatures of Singularities in Simplicial Ricci Flow

摘要: We apply the methods of persistent homology to a selection two and three--dimensional geometries evolved by simplicial Ricci flow. To implement homology, we construct triangular mesh for sample points. The scalar curvature along edges triangulation, computed as an average curvatures at endpoints edges, serves filtration parameter each time step. present analyze results application two--dimensional rotational solid that collapses dumbbells manifest neckpinch singularities. compare appearance critical geometric phenomena in these models with conclude does indicate criticality. Finally, discuss interpretation implication future applications.