Timeline for The maximum number of vertical independent vector fields on the tangent bundle

13 events

when toggle format	what		by	license	comment
Dec 22, 2020 at 23:34	history	edited	Ali Taghavi	CC BY-SA 4.0	deleted 181 characters in body
Dec 22, 2020 at 23:34	vote	accept	Ali Taghavi
Dec 22, 2020 at 20:49	history	edited	Ali Taghavi	CC BY-SA 4.0	added 185 characters in body
Dec 19, 2020 at 21:39	history	became hot network question
Dec 19, 2020 at 17:18	history	edited	Ali Taghavi	CC BY-SA 4.0	edited body
Dec 19, 2020 at 17:13	history	edited	Ali Taghavi	CC BY-SA 4.0	added 14 characters in body
Dec 19, 2020 at 17:04	history	edited	Ali Taghavi	CC BY-SA 4.0	added 14 characters in body
Dec 19, 2020 at 16:51	history	edited	Ali Taghavi	CC BY-SA 4.0	added 387 characters in body
Dec 19, 2020 at 14:29	history	edited	Michael Albanese	CC BY-SA 4.0	deleted 30 characters in body; edited tags
Dec 19, 2020 at 14:09	answer	added	Michael Albanese		timeline score: 10
Dec 19, 2020 at 14:06	comment	added	Bertram Arnold		A vector bundle has $k$ independent vector fields iff its classifying map lifts from $BO(n)$ to $BO(n-k)$. In your case, this is the composition of the classifying map of $TM$ with the projection to $M$, which is a homotopy equivalence. For spheres, this is known explicitly, cf en.m.wikipedia.org/wiki/Vector_fields_on_spheres Integrable distributions can probably also be described explicitly using Haefliger's theorem.
Dec 19, 2020 at 13:46	history	edited	Ali Taghavi	CC BY-SA 4.0	added 82 characters in body
Dec 19, 2020 at 13:37	history	asked	Ali Taghavi	CC BY-SA 4.0