2 citations · 2 across the 4 of their papers we have counts for
8 papers
Function-Rips complexes in persistent homotopy theory: Stability and persistent Latschev theorems
Steve Oudot, Lukas Waas
Classical results of Hausmann and Latschev show that Vietoris-Rips complexes can recover the homotopy type of a manifold, even from finite metric spaces that are nearby in Gromov-H…
Notes on abelianity of categories of finitely encoded persistence modules
Lukas Waas
When working with (multi-parameter) persistence modules, one usually makes some type of tameness assumption in order to obtain better control over their algebraic behavior. One suc…
On stratifications and poset-stratified spaces
Lukas Waas, Jon Woolf, Shoji Yokura
A stratified space is a topological space equipped with a \emph{stratification}, which is a decomposition or partition of the topological space satisfying certain extra conditions.…
Presenting the topological stratified homotopy hypothesis
Lukas Waas
This article is concerned with three different homotopy theories of stratified spaces: The one defined by Douteau and Henriques, the one defined by Haine, and the one defined by Na…
Combinatorial models for stratified homotopy theory
Lukas Waas
This paper is part of a series of three articles with the objective of investigating a stratified version of the homotopy hypothesis in terms of semi-model structures that interact…
On the homotopy links of stratified cell complexes
Lukas Waas
Homotopy links have proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy link…