On Vietoris-Rips complexes of ellipses

For X a metric space and r>0 a scale parameter, the Vietoris-Rips complex VR_<(X;r) (resp. VR_≤(X;r)) has X as its vertex set, and a finite subset σ⊆ X as a simplex whenever the diameter of σ is less than r (resp. at most r). Though Vietoris-Rips complexes have been studied at small choices of scale by Hausmann and Latschev, they are not well-understood at larger scale parameters. In this paper we investigate the homotopy types of Vietoris-Rips complexes of ellipses Y={(x,y)∈ℝ^2 | (x/a)^2+y^2=1} of small eccentricity, meaning 1更多