2 citations · 2 across the 11 of their papers we have counts for
11 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…
From Samples to Persistent Stratified Homotopy Types
Tim Mäder, Lukas Waas
The natural occurrence of singular spaces in applications has led to recent investigations on performing topological data analysis (TDA) in a stratified framework. In many applicat…
From homotopy links to stratified homotopy theories
Sylvain Douteau, Lukas Waas
In previous work, the first author defined homotopy theories for stratified spaces from a simplicial and a topological perspective. In both frameworks stratified weak-equivalences…
A property of the interleaving distance for sheaves
Francois Petit, Pierre Schapira, Lukas Waas
Let be a real analytic manifold endowed with a distance satisfying suitable properties and let be a field. In [PS20], the authors construct a pseudo-distance on th…
Amplitudes in persistence theory
Barbara Giunti, John S. Nolan, Nina Otter +1
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants…
Stratified Homotopy Theory and a Whitehead Group for Stratified Spaces
Lukas Waas
In this master thesis, we extend results from classical simple homotopy theory to the world of stratified homotopy theory. To obtain a well-established framework to work in, we pro…