Talk:Homotopy

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	B Class	Top Priority	Field: Topology
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. At the moment this is the main article on homotopy theory. Geometry guy 19:52, 10 June 2007 (UTC)

I think it is not true as stated in the article, that when X and Y are homotopy equivalent, and X is locally path connected, then Y is also locally path connected. For an example, take the subspace of a unit square consisting of the interval [(0,0),(0,1)] together with all line segments from (0,1) to the points (1/n,0) where n runs through all natural numbers. The space is contractible, but it is not locally path connected at (0,0).

I am not sure that the statement that two homotopies can be rotated makes much sense (but I know what is meant..:) )

Yes, locally path-connected isn't a homotopy invariant.

It seems to me the stuff on homotopy groups belongs in its own article. --gorlim 16:52, 24 Apr 2004 (UTC)

The stuff on homotopy groups has its own page. It seems to me that the stuff on isotopy belongs in its own article. —Blotwell 08:40, 23 July 2005 (UTC)

Misleading picture?

The illustration with caption "An illustration of a homotopy between the two bold paths" is somewhat confusing for two reasons:

1. first, which subsets of the bold loop correspond to the "two bold paths" could be misinterpreted, making the isolines even more confusing

2. second, at first glance, the illustration makes you think that all homotopies are necessarily relative to some none-empty subset, since the endpoints of the curves are fixed.

I'm changing the caption for reason #2, feel free to change it back...

I think the etimology here is wrong: homo-topy comes from the greek verb "topao"(= to melt, or to deform), and not from the name "topos" (= place).

(in reference to above) was the etymology clarified? 68.239.20.246 00:29, 22 June 2007 (UTC)

Why are all the illustrations isotopies??

Would be nice if someone would create/add an illustration of a homotopy that's not an isotopy :)