# Talk:Morse theory

WikiProject Mathematics (Rated C-class, Mid-priority)
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Mathematics rating:
 C Class
 Mid Priority
Field: Topology

I noticed that the figure of the torus has not the labels of the points corresponding to p, q, r,... Just take a look at the paragraph which starts as: "When a is less than 0", it makes reference to the points above, but one can not find them displayed on any picture. Thank you --Dieu reconnaîtra les siens 00:42, 28 March 2009 (UTC) —Preceding unsigned comment added by Kriega (talkcontribs)

## Contents

Hi; I'm trying desperately to understand many of these advanced principals of mathematics, such as Morse theory, but no matter how many times I review the material, it doesn't sink in. Could someone please provide examples, problems to solve (with their solutions) and/or ways to visualize this? beno 26 Jan 2006

## Other generalisations

It seems to me that this article might benefit from a discussion of Smale's take on Morse theory (using handles) and also Morse-Smale-Witten theory (critical points of index k generate the k-chains in a chain complex with boundary operator given by \delta : C_{k} \rightarrow C_{k - 1} that sends a critical point of index k to a sum of the critical points of index k - 1 reachable by paths from that point counted with degeneracy. However it is also possible that this will just obfuscate the general message of the article and will just make things too complex, so I merely choose to mention this in passing rather than perform edits myself.RogueTeddy 06:18, 29 June 2007 (UTC)

Nevermind, I see that this has already been done. I have updated the "see also" links on the main article accordingly.RogueTeddy 06:24, 29 June 2007 (UTC)

## Not porous

I changed the Basic Concepts section to read "Assume the ground is not porous" (it used to say "Assume the ground is porous"), as this seems to me the only way it could make sense. We want the water to flood the landscape up to a certain elevation a and not sink into the soil, so that we can say the flooded portion is the inverse image of (-∞, a]. Idempotent (talk)

>I changed it back to the original wording and added a clarificaiton. I agree it does sounds like the water would just flow away, but the reason for the porosity is to ensure the water can can access lower elevation areas which are landlocked. To ensure only a finite amout of water is needed it might be better to think of this scenario like a fish tank with a sandy landscape in it.

## Cayley and Maxwell

hi, could someone put in a reference for the connection to cayley and maxwell? it would be great to know exactly what this contributor is talking about. i've never heard of this reference before. — Preceding unsigned comment added by 24.34.193.55 (talk) 20:20, 2 August 2012 (UTC)