English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Multidimensional persistence has been proposed to study the persistence oftopological features in data indexed by multiple parameters. In this work, wefurther explore its algebraic complications from the point of view of higherdimensional indecomposable persistence modules containing lower dimensionalones as hyperplane restrictions. Our previous work constructively showed thatany finite rectangle-decomposable $n$D persistence module is the hyperplanerestriction of some indecomposable $(n+1)$D persistence module, as a corollaryof the result for $n=1$. Here, we extend this by dropping the requirement ofrectangle-decomposability. Furthermore, in the case that the underlying fieldis countable, we construct an indecomposable $(n+1)$D persistence modulecontaining all $n$D persistence modules, up to isomorphism, as hyperplanerestrictions. Finally, in the case $n=1$, we present a minimal constructionthat improves our previous construction.

The Whole in the Parts: Putting $n$D Persistence Modules Inside Indecomposable $(n + 1)$D Ones