---- > [!definition] Definition. ([[exterior bundle]]) > Let $M$ be a [[smooth manifold]], and let $p \in M$. The **exterior bundle** of $M$ is the [[vector bundle]] $\Lambda^{\bullet}T^{*}M$ given by $\Lambda^{\bullet}T^*M = \coprod_{p \in M} \Lambda^{\bullet}T^*_{p}M,$ where $\Lambda^{\bullet}T_{p}^{*}M = \bigoplus_{r \in \mathbb{Z}_{\geq 0}}\Lambda^{r} T_{p}^{*}M$ > and $\Lambda^{r}T_{p}^{*}M$ denotes the [[exterior algebra]] over the [[cotangent space]] of $M$ at $p$. ^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 > ```