Lesson plan
Subbundle
In mathematics, a subbundle L of a vector bundle E over a topological space M is a subset of E such that for each x in M, the set L_x , the intersection of the fiber E_x with L , is a vector subspace of the fiber E_x so that L is a vector bundle over M in its own right. In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors). If locally, in a neighborhood N_x of x \in M , a set of vector fields Y_k span the vector spaces L_y, y \in N_x, and all Lie commutators \left[Y_i, Y_j\right] are linear combinations of Y_1, \dots, Y_n then one says that L is an involutive distribution.
Article summary
In mathematics, a subbundle L of a vector bundle E over a topological space M is a subset of E such that for each x in M, the set L_x , the intersection of the fiber E_x with L , is a vector subspace of the fiber E_x so that L is a vector bundle over M in its own right. In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors). If locally, in a neighborhood N_x of x \in M , a set of vector fields Y_k span the vector spaces L_y, y \in N_x, and all Lie commutators \left[Y_i, Y_j\right] are linear combinations of Y_1, \dots, Y_n then one says that L is an involutive distribution.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.