Talk:Handle decomposition

New To Advanced Math
Hi; I'm trying desperately to understand many of these advanced principals of mathematics, such as handle decomp, 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

Hint for learning about handle decompositions
Hello,

obviously these pages are written by non-experts. So if you want to understand handle decompositions and surgeries on manifolds I strongly advise you to not read this pages. Instead look into the following book:

R.E. Gompf and A.I. Stipsicz, 4-Manifolds and Kirby Calculus, American Math. Soc. (1999).


 * I briefly scanned the article. Yup, it's not in good health. Rybu (talk) 19:44, 14 November 2009 (UTC)

Pictures
I think that any good topological article should include some manner of picture to accompany it's analytic standpoint. The founders of the field have the unfair advantage of starting with the pictures and slowly building the algebraic and analytic structures, but those beginning are asked to bypass the visual aspects which are central to the study of topology (one might even say that's the whole point). If anyone has some manner of (public domain) images he could upload, I think that would greatly increase the value of this article. Guardian of Light 15:25, 3 October 2007 (UTC)

Rewrite
I'm not happy with this page and I want to rewrite pretty much the entire article. The direction I want to go with it is to show how handle decompositions are the natural way to adapt CW-structures to the world of smooth manifolds. Okay, so I've done some major revisions but there still some things todo:


 * Smoothing of corners issue.
 * handle presentations of cobordisms
 * dual handle presentations,
 * surgery and h-cobordism links,
 * comparison to Whitehead's theorems about reducing the cell structure of CW-complexes.
 * the handle decomposition interpretation of Poincare duality.
 * more diagrams would be helpful. We can probably poach some from various surgery / cw-complex related pages, too.

That's all for now. Rybu (talk) 23:21, 18 November 2009 (UTC)