3 papers
math.AT2026
A continuum of Künneth theorems for persistence modules
Nikola Milićević
We develop new aspects of the homological algebra theory for persistence modules, in both the one-parameter and multi-parameter settings. For a poset and an order preserving ma…
math.AT2024
The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs
Nikola Milićević, Nicholas A. Scoville
We prove analogues of classical results for higher homotopy groups and singular homology groups of pseudotopological spaces. Pseudotopological spaces are a generalization of (Čech)…
math.AT2023
Singular homology of roots of unity
Nikola Milićević
We extend some basic results from the singular homology theory of topological spaces to the setting of Čech's closure spaces. We prove analogues of the excision and Mayer-Vietoris…