---- > [!definition] Definition. ([[smooth submersion]]) > Let $M,N$ be [[smooth manifold|smooth manifolds]], $F:M \to N$ a [[smooth maps between manifolds|smooth map]]. We say $F$ is a **submersion at $p \in M$** if $dF_{p}:T_{p}M \to T_{F(p)}M$ is a [[surjection]]. In this case, $p$ is called a **regular point** of $F$; otherwise $p$ is called a **critical point** of $F$. A point $q \in N$ is a **regular value** if the [[level set]] $F ^{-1}(q)$ consists of only regular points. > If $F$ is a [[smooth submersion]] at each $p \in M$, then we say $F$ is a **submersion**. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```