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/

Zendy Plus

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

Zendy Tools

Zendy Open

We prove a discrete version of the Lusternik-Schnirelmann theorem fordiscrete Morse functions and the recently introduced simplicialLusternik-Schnirelmann category of a simplicial complex. To accomplish this, anew notion of critical object of a discrete Morse function is presented, whichgeneralizes the usual concept of critical simplex (in the sense of R. Forman).We show that the non-existence of such critical objects guarantees the stronghomotopy equivalence (in the Barmak and Minian's sense) between thecorresponding sublevel complexes. Finally, we establish that the number ofcritical objects of a discrete Morse function defined on $K$ is an upper boundfor the non-normalized simplicial Lusternik-Schnirelmann category of $K$.

Strong discrete Morse theory and simplicial L-S category: A discrete version of the Lusternik-Schnirelmann Theorem