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math.AT2023
Directed Homology and Persistence Modules
Eric Goubault
In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural…
math.AT2023★ 1 cited
Persistent homology of partially ordered spaces
Cameron Calk, Eric Goubault, Philippe Malbos
In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces,…
math.AT2023
A semi-abelian approach to directed homology
Eric Goubault
We develop a homology theory for directed spaces, based on the semi-abelian category of (non-unital) associative algebras. The major ingredient is a simplicial algebra constructed…