Talk:Submersion (mathematics)

I think the introduction to this topic should be changed to the following.

In mathematics, a differentiable map f from an m-manifold M to an n-manifold N is said to be a submersion, if its differential is a surjective map at every point p of M, or equivalently, if rank Df(p) = dim N = n.

Ahsan

Why? The intorduction, as it stands, offers far more detail and explanation that your proposed introduction. Dharma6662000 (talk) 04:00, 25 August 2008 (UTC)

Submersion Theorem

I deleted the submersion theorem. It seemed to have been tacked on with a later edit. Its notation didn't match the original article (e.g. using $x^0$ instead if p to denote a point in the source manifold). Secondly there was absolutely no attempt to say what the notation meant, or to link it. For example writing thinks like $\mbox{Lin}(\mathbb{R}^n,\mathbb{R}^{n-d})$ without saying that it was the space of linear maps from $\mathbb{R}^n$ to $\mathbb{R}^{n-d}$. I understood what that means because I understand the idea. But there were other random notations like $N(x^0)$ that even I didn't understand. This theorem needs to be rewriten by someone that has some sympathy for the reader. I'll try to do it tomorrow. Dharma6662000 (talk) 04:00, 25 August 2008 (UTC)

Morse theory

The final paranthetical remark is misleading: in Morse theory N = R so a critical point (in the sense of not being a submersion) is one where df has rank less than 1, that is df = 0. There is therefore no situation where f is neither critical nor a submersion (sorry - too many negatives!) I will remove this if no-one objects. Simplifix (talk) 14:38, 2 March 2009 (UTC)

I agree with you. 81.182.216.220 (talk) 01:03, 10 March 2009 (UTC)

Simplifix, I guess you mean that f is always either a submersion in a sufficiently small neighbourhood of some point x or that x is a critical point of f. If that's what you mean then I agree.  Δεκλαν Δαφισ   (talk)  21:03, 10 March 2009 (UTC)