7 citations · 19 across the 9 of their papers we have counts for
9 papers
Metric spaces and homotopy types
J. F. Jardine
By analogy with methods of Spivak, there is a realization functor which takes a persistence diagram in simplicial sets to an extended pseudo-metric space (or ep-metric space) $…
Stability for UMAP
J. F. Jardine
This paper displays the Healy-McInnes UMAP construction as an iterated pushout of Vietoris-Rips objects associated to extended pseudo metric spaces (ep-metric spaces) defi…
Persistent homotopy theory
J. F. Jardine
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms.…
Path categories and quasi-categories
J. F. Jardine
This paper gives an introduction to the homotopy theory of quasi-categories. Weak equivalences between quasi-categories are characterized as maps which induce equivalences on a nat…
Data and homotopy types
J. F. Jardine
This paper presents explicit assumptions for the existence of interleaving homotopy equivalences of both Vietoris-Rips and Lesnick complexes associated to an inclusion of data sets…
Cosimplicial spaces and cocycles
J. F. Jardine
Standard results from non-abelian cohomology theory specialize to a theory of torsors and stacks for cosimplicial groupoids. The space of global sections of the stack completion of…