Evolution of the magnetic fields of solar flare active regions from the geometry and topology of HMI/SDO magnetograms

The testing and development of topological approaches to the analysis of solar magnetic fields are considered. A technique based on the geometry of random fields, mathematical morphology and topology, and scale-space analyses are applied to describe and diagnose the pre-flare dynamics of the magnetic fields of solar active regions using HMI/SDO magnetograms. The results show that this formalism can be used to diagnose pre-flare dynamics over time intervals that are of practical interest.