3 papers
math.RT2020
The Whole in the Parts: Putting D Persistence Modules Inside Indecomposable D Ones
Mickaël Buchet, Emerson G. Escolar
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebra…
math.RT2019
Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
Mickaël Buchet, Emerson G. Escolar
A recent work by Lesnick and Wright proposed a visualisation of D persistence modules by using their restrictions onto lines, giving a family of D persistence modules. We giv…
math.AT2018
Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
Mickaël Buchet, Emerson G. Escolar
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is th…