3 papers
math.AT2026
A constructive proof for the simple connectedness of finite subset spaces
JÄnis Lazovskis
The space of all finite non-empty subsets of a topological space , also known as the Ran space of , is weakly contractible for path connected. We consider subspaces $\mat…
math.AT2026
Pruning vineyards: updating barcodes and representative cycles by removing simplices
Barbara Giunti, JÄnis Lazovskis
The barcode of a filtration and its representative cycles encode rich information often useful in data analysis. However, obtaining them can be computationally expensive. Therefore…
math.AT2025
Stability of 0-dimensional persistent homology in enriched and sparsified point clouds
JÄnis Lazovskis, Ran Levi, Juliano Morimoto
We give bounds for dimension 0 persistent homology and codimension 1 homology of Vietoris--Rips, alpha, and cubical complex filtrations from finite sets related by enrichment (addi…