121 citations · 278 across the 14 of their papers we have counts for
14 papers
The Simplicial Loop Space of a Simplicial Complex
Gregory Lupton, Jonathan Scott
Given a simplicial complex , we construct a simplicial complex that may be regarded as a combinatorial version of the based loop space of a topological space. Our construct…
Exact weights, path metrics, and algebraic Wasserstein distances
Peter Bubenik, Jonathan Scott, Donald Stanley
We use weights on objects in an abelian category to define what we call a path metric. We introduce three special classes of weight: those compatible with short exact sequences; th…
Interleaving and Gromov-Hausdorff distance
Peter Bubenik, Vin de Silva, Jonathan Scott
One of the central notions to emerge from the study of persistent homology is that of interleaving distance. It has found recent applications in symplectic and contact geometry, sh…
Metrics for generalized persistence modules
Peter Bubenik, Vin de Silva, Jonathan Scott
We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form…
Categorification of persistent homology
Peter Bubenik, Jonathan A. Scott
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some t…
Twisting structures and strongly homotopy morphisms
Kathryn Hess, Jonathan Scott
In an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degree…