110 citations · 163 across the 22 of their papers we have counts for
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math.AT2022★ 1 cited
A Sheaf-Theoretic Construction of Shape Space
Shreya Arya, Justin Curry, Sayan Mukherjee
We present a sheaf-theoretic construction of shape space -- the space of all shapes. We do this by describing a homotopy sheaf on the poset category of constructible sets, where ea…
math.AT2022
A Lattice-Theoretic Perspective on the Persistence Map
Brendan Mallery, Adélie Garin, Justin Curry
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our d…