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It seems to me that something isn't correct here:
I think that if π:E→M , then dπ:TE→TM and not TE→π*TM.
π*TM is the pullback bundle, so that dπ : TE → π*TM is a morphism of vector bundles over E. Whereas, thinking of it as dπ : TE → TM, it is a mapping which covers π, so that the pair (dπ, π) is a vector bundle morphism. I have seen both in the literature, but the first way it is slightly more precise. silly rabbit ( talk) 11:37, 13 March 2008 (UTC)
I am not an expert, but, are we assumming here that the top space E is a manifold or at least that the fibers over individual points are manifolds? I say this because we are referring here first of all to TE , which assumes E is a manifold, and then we refer to T_e(E_x) , where E_x is the fiber over x , i.e., we have π(e)=x , and then we consider E_x:=π^{-1}(x) , and then T_e(E_x) , so E_x must be a manifold, to have a tangent space? — Preceding unsigned comment added by 146.96.35.67 ( talk) 07:58, 30 May 2013 (UTC)
In Jan 2016, User:TakuyaMurata proposed that Horizontal bundle be merged into this article, with the note: better to discuss the two complementary concepts at the same place; less repetition, especially.
I'm concerned about this proposal; these are related ideas, they focus on very different things. For example:
Doing all this ... well. Hmm. Might not be a bad idea. Changing my mind, maybe I will merge. 67.198.37.16 ( talk) 17:49, 22 April 2016 (UTC)
The result of the move request was: moved ( non-admin closure) KSF T C 19:24, 18 May 2016 (UTC)
Vertical bundle →
Vertical and horizontal bundles – The article covers both the vertical and horizontal bundles in a unified way, rather than each, individually
67.198.37.16 (
talk) 18:13, 30 April 2016 (UTC) --Relisted.
George Ho (
talk)
06:12, 8 May 2016 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
This topic is in need of attention from an expert on the subject. The section or sections that need attention may be noted in a message below. |
It seems to me that something isn't correct here:
I think that if π:E→M , then dπ:TE→TM and not TE→π*TM.
π*TM is the pullback bundle, so that dπ : TE → π*TM is a morphism of vector bundles over E. Whereas, thinking of it as dπ : TE → TM, it is a mapping which covers π, so that the pair (dπ, π) is a vector bundle morphism. I have seen both in the literature, but the first way it is slightly more precise. silly rabbit ( talk) 11:37, 13 March 2008 (UTC)
I am not an expert, but, are we assumming here that the top space E is a manifold or at least that the fibers over individual points are manifolds? I say this because we are referring here first of all to TE , which assumes E is a manifold, and then we refer to T_e(E_x) , where E_x is the fiber over x , i.e., we have π(e)=x , and then we consider E_x:=π^{-1}(x) , and then T_e(E_x) , so E_x must be a manifold, to have a tangent space? — Preceding unsigned comment added by 146.96.35.67 ( talk) 07:58, 30 May 2013 (UTC)
In Jan 2016, User:TakuyaMurata proposed that Horizontal bundle be merged into this article, with the note: better to discuss the two complementary concepts at the same place; less repetition, especially.
I'm concerned about this proposal; these are related ideas, they focus on very different things. For example:
Doing all this ... well. Hmm. Might not be a bad idea. Changing my mind, maybe I will merge. 67.198.37.16 ( talk) 17:49, 22 April 2016 (UTC)
The result of the move request was: moved ( non-admin closure) KSF T C 19:24, 18 May 2016 (UTC)
Vertical bundle →
Vertical and horizontal bundles – The article covers both the vertical and horizontal bundles in a unified way, rather than each, individually
67.198.37.16 (
talk) 18:13, 30 April 2016 (UTC) --Relisted.
George Ho (
talk)
06:12, 8 May 2016 (UTC)