Alexander McCleary (10/02/24): Persistent Homology for Infinite Complexes

Описание к видео Alexander McCleary (10/02/24): Persistent Homology for Infinite Complexes

Abstract: Persistent homology is a powerful tool for understanding the evolution of homological features in a filtered CW complex. Traditionally, its theory has been limited to finite complexes. In this talk, we will present a theoretical framework that extends persistent homology to infinite CW complexes. We will also demonstrate that the two cornerstone theorems of persistent homology—the Bottleneck Stability Theorem and the Algebraic Decomposition Theorem—hold without the need for finiteness assumptions. This extension opens new avenues for applying persistent homology to a broader class of problems in topological data analysis.

Комментарии

Информация по комментариям в разработке

Похожие видео