Peter Goričan: Reduced Vietoris-Rips Complexes, part 2

In the seminar we will first define RNG graphs (relative neighborhood graphs), with the help of which we will prove some properties for Rips com- plexes, and then we will define a reduced Rips complex and show the con- nection with the Rips complex. Finally, we will look at the algorithm for computing one-dimensional persistent homology on reduced Rips complexes.