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

Let $Crit M$ denote the minimal number of critical points (not necessarilynon-degenerate) on a closed smooth manifold $M$. We are interested in theevaluation of $Crit$. It is worth noting that we do not know yet whether $CritM$ is a homotopy invariant of $M$. This makes the research of $Crit$ achallenging problem.  In particular, we pose the following question: given a map $f: M \to N$ ofdegree 1 of closed manifolds, is it true that $Crit M \geq Crit N$? We provethat this holds in dimension 3 or less. Some high dimension examples areconsidered. Note also that an affirmative answer to the question implies thehomotopy invariance of $Crit$; this simple observation is a good motivation forthe research.

Maps of Degree One, Lusternik Schnirelmann Category, and Critical Points