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Browsing Mathematik by Author "Adamaszek, Michal"
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- ItemOn Vietoris-Rips complexes of ellipses(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Adamaszek, Michal; Adams, Henry; Reddy, SamadwaraFor 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 [12, 14], 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)∈R2|(x/a)2+y2=1} of small eccentricity, meaning 1