Talk:Closed and exact differential forms

message: I would find it clearer to say:
Since d^2 = 0, to be closed is a necessary condition to be exact. Asking whether this is also a sufficient condition is a way of detecting topological information, by differential conditions.
The argument is that it is usually easy to test da=0 and hard to find b with db=a.
: Be bold! If you feel it's best to change, change it, by all means. Dysprosia 10:25, 5 Feb 2004 (UTC)
thread_title: Better wording

message: This is a nice short article focused on explaining one concept, so it should stay this way. I don't see how this would be made better if part of a bigger article.
What this article needs is an expansion. It neeeds to be made more clear what exactly closedness means, some examples, and a counterexample of a closed form which is not exact. 
MarSch, please read Wikipedia_talk:WikiProject_Mathematics#Math_in_the_dock. The biggest problem of math on Wikipedia is that it is too hard to understand for people who know less than the author of an article. So let us try to make things more accessible, not less. Oleg Alexandrov 16:01, 14 September 2005 (UTC)
replies: text: Agree with Oleg. Also, this article can be expanded, as it is the doorway to homology and cohomology and harmonic forms and all that. linas 01:05, 15 September 2005 (UTC)
thread_title:  Disagree with merging of this into [[differential form]] 

message: Isn't there an error of sign in the expression for d\alpha where \alpha is a one form on the plane? (anonymous) 11:26, 6 October 2005 (UTC)
replies: text: Different authors have different sign conventions; but you are right, it it disagrees with the convention used in exterior derivative.  linas 23:52, 7 October 2005 (UTC)
thread_title:  Error of sign? 

message: The article of gauge transformation says:
Mathematically, a gauge is just a choice of a (local) section of some principal bundle. A gauge transformation is just a transformation between two such sections.
The introduction part of the present article says:
The form β is called a "potential form" or "primitive" for α. Since d2 = 0, β is not unique, but can be modified by the addition of the differential of a two-step-lower-order form. This is called gauge transformation.
Is it correct? Is it true that this is generally some gauge transformation? Because if yes, then there sholud be somwhere a brincipal bundle and a section. Where are they?89.135.29.163 (talk) 06:16, 4 March 2011 (UTC)
thread_title:  Gauge transformation 

message: The definition given of the Poincare lemma states in part: '...any smooth closed p-form α defined on X is exact...'.
Is the smooth property redundant? Aren't all differential forms smooth? 130.95.51.206 (talk) 04:37, 30 September 2012 (UTC)
thread_title:  Poincare Lemma, is 'smooth' redundant? 

message: It is my understanding that kernels make sense only for linear maps , i.e., for 1-forms.
For k-linear maps defined on W:=VxVxVx..xV, the kernel is not a subspace of W. Should one then
talk about the kernel of a k-form in general, or just about the kernel of a 1-form?  — Preceding unsigned comment added by 150.210.231.36 (talk) 21:42, 31 July 2014 (UTC)
thread_title:  Kernel of a Form?