Under explicit density and scale-gap assumptions, including a data set into a larger one induces homotopy equivalences of Vietoris-Rips and Lesnick complexes, and a controlled homotopy equivalence of branch point posets.
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Data and homotopy types
Under explicit density and scale-gap assumptions, including a data set into a larger one induces homotopy equivalences of Vietoris-Rips and Lesnick complexes, and a controlled homotopy equivalence of branch point posets.