Talk:Homotopy group

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Hey, you... I think Homotopy groups is a more appropriate page, and this one can be a redirect, yes?

We need to fix a whole lot of links now, either way.

It has been homology group, for a long time. By the way, moving a page does create a redirect.

Charles Matthews 12:22, 27 May 2004 (UTC)

It's my understanding that the convention is to always use the singular unless there is some compelling reason to use the plural. For example, a compelling reason would be "orthogonal polynomials"; here you must have the plural because the definition of the term doesn't make sense for a single polynomial. In this case, although the homotopy groups are often studied all at once collectively, the object of "a homotopy group" is meaningful and not nonsensical, so I think this is best. Revolver 07:18, 22 Jun 2004 (UTC)

[edit] Equivalent spheres in a space are ... what?

From the article:

The many different ways to (continuously) map an n-dimensional sphere into a given space are collected into equivalence classes, called homotopy classes. Two mappings are homotopy equivalent if one can be continuously deformed into the other.

(Emphasis added.) Aren't they homotopic, rather than homotopy equivalent? (See Homotopy for definition of homotopy equivalent.) —msh210 19:35, 23 Nov 2004 (UTC)

Definitely should be homotopic; I have changed it.

Neil Strickland (a topologist) 19:44, 23 Nov 2004 (UTC)

Right, maps are homotopic, spaces homotopy equivalent. Charles Matthews 20:14, 23 Nov 2004 (UTC)