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A picture would be very helpful in explaining what the handleboy thing is, I think. Oleg Alexandrov 17:44, 25 Jun 2005 (UTC)

If there are some Properties List here, I think there are much conveninence to the reader.

This page only discusses 1-handles. Sometime someone who has interest and a reference or two might add the general definition of an n-dimensional k-handle and give more examples, eventually causing the content of the current page to become an example. Orthografer 20:05, 14 June 2006 (UTC)[reply]

Hi there! In the 3-handlebody section, the reader can read this: "As a bit of notation, the genus of V is the genus of the surface which forms the boundary of V."

this result seems very useful for me. Could you provide a reference to a book/paper showing that?

I mean: is the genus of the boundary of V equal the maximal number of non-intersecting embedded 2-discs that cut V without rendering it disconnected?

thanks for your answers guys

j. —Preceding unsigned comment added by 155.98.20.227 (talk) 21:49, 4 December 2008 (UTC)[reply]

The answer to your question "is the genus of the boundary of V equal the maximal number of non-intersecting embedded 2-discs that cut V without rendering it disconnected?" is yes. I don't have a reference handy. But it is not so hard to prove. best, Sam nead (talk) 20:49, 7 December 2008 (UTC)[reply]

Thx for the confirmation. Actually, I wanted to have a reference because I'm either too lazy to prove it or just too idiot.

anyway, I guess even a reference in the handlebody article wouldn't hurt.

j. —Preceding unsigned comment added by 24.10.251.154 (talk) 01:56, 8 December 2008 (UTC)[reply]

Here's a reference which seems interesting to me and which could be worth a citation in the article:

"Computing Homology Groups of Simplicial Complexes in R^3", Tamal K. Dey and Sumanta Guha, Journal of the ACM 45(2), pp. 266-287, 1998

j. —Preceding unsigned comment added by 155.98.20.227 (talk) 16:43, 11 December 2008 (UTC)[reply]

I don't see a reason why this article is separate from handle decomposition, since these really describe the same concept. I think they should be merged. --TurionTzukosson (talk) 12:13, 8 May 2018 (UTC)[reply]

The first sentence of the article is this:

"In the mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces."

No, it is not.

That is called a "handlebody decomposition" (not just a "handlebody"). 2601:200:C000:1A0:4031:3F87:AF33:5852 (talk) 03:58, 8 February 2022 (UTC)[reply]

The following appears in the article:

"For instance, a handlebody decomposition completely describes the manifold up to homeomorphism. In dimension four, they even describe the smooth structure, as long as the attaching maps are smooth. This is false in higher dimensions; any exotic sphere is the union of a 0-handle and an n-handle."

This makes no sense at all, because the concept of "a handlebody decomposition" has not been clearly defined anywhere in the article.

If such a decomposition includes the glueing maps, then certainly (in any dimension) the smooth structure is described by the handlebody decomposition. 2601:200:C000:1A0:4031:3F87:AF33:5852 (talk) 04:05, 8 February 2022 (UTC)[reply]