Identifying cobordisms using kernel persistence

TL;DR

This paper introduces a homological approach to identify cobordisms in filtered complexes, utilizing kernel persistence and matrix reduction to determine their birth and death times, with applications in chemistry.

Contribution

It presents a novel homological definition of cobordisms and a method using kernel persistence for their detection in filtered complexes.

Findings

Provides a new homological framework for cobordisms.

Develops a matrix reduction algorithm for pairing birth and death times.

Applicable to chemical data analysis.

Abstract

Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times.