Vietoris-Rips metric thickenings of the circle (Q6061910)

The novelty of the paper is the use of the Vietoris-Rips metric thickenings as an alternate approach to understanding Vietoris-Rips simplicial complexes and their persistent homology. The author especially confirms some conjectures that have been made about the homotopy types and barcodes of the Vietoris-Rips simplicial complexes of the circle. More precisely, he proves that the Vietoris-Rips metric thickenings of the circle are homotopy equivalent to odd-dimensional spheres at the expected scale parameters.