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pro vyhledávání: '"Waas, Lukas"'
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. More recently, the notion of poset-stratified space, i.e., topologica
Externí odkaz:
http://arxiv.org/abs/2407.17690
Autor:
Waas, Lukas
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 such notion is Ezra Millers notion of finite encodability, which roughly
Externí odkaz:
http://arxiv.org/abs/2407.08666
Autor:
Waas, Lukas
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 Nand-Lal. One of the central questions concerning these theories has bee
Externí odkaz:
http://arxiv.org/abs/2403.07686
Autor:
Waas, Lukas
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 semimodel structures that interact well with classical examples of stratified spaces, such as Whitney str
Externí odkaz:
http://arxiv.org/abs/2403.06280
Autor:
Waas, Lukas
Homotopy links haven proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy links of a stratified simplicial set. For many purposes, in particular to
Externí odkaz:
http://arxiv.org/abs/2403.06272
Autor:
Mäder, Tim, Waas, Lukas
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 applications, there is no a priori information on what points should be regard
Externí odkaz:
http://arxiv.org/abs/2206.08926
Autor:
Douteau, Sylvain, Waas, Lukas
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 are detected by suitable generalizations of homotopy links. These two
Externí odkaz:
http://arxiv.org/abs/2112.02394
Publikováno v:
In Journal of Pure and Applied Algebra December 2024 228(12)
Let $X$ be a real analytic manifold endowed with a distance satisfying suitable properties and let $\mathbf{k}$ be a field. In [PS20], the authors construct a pseudo-distance on the derived category of sheaves of $\mathbf{k}$-modules on $X$, generali
Externí odkaz:
http://arxiv.org/abs/2108.13018
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 that one associates with data sets. Here we introduce a general frame
Externí odkaz:
http://arxiv.org/abs/2107.09036