Definition talk:Homotopy

I second the suggestion that free homotopy be assigned a separate subpage. --Lord_Farin (talk) 20:26, 23 October 2012 (UTC)


 * By "free homotopy" don't you mean "relative homotopy", which I got to just before you posted that? --prime mover (talk) 20:32, 23 October 2012 (UTC)


 * No. It's awkward to have the general as a subpage of the specific in a definition. I think the page should be split so that both can be referred to independently and unambiguously. --Lord_Farin (talk) 21:45, 23 October 2012 (UTC)


 * If you know anything about this stuff you know more about it than me. Do what you think needs to be done. --prime mover (talk) 21:33, 24 October 2012 (UTC)


 * I deny being knowledgeable - I'm just taking a course on it now, that's all. I just commented on the site-structural side, for which it sufficed to notice that the subpage currently holds a more general (and conceptually different) definition than the main page. That's all; I'll fix the subpage. --Lord_Farin (talk) 21:35, 24 October 2012 (UTC)
 * Done. --Lord_Farin (talk) 21:47, 24 October 2012 (UTC)

Regarding Also known as: in case of ambiguity, "homotopic" is almost universally used for "homotopic relative to the things that ought to be fixed". For example, homotopy between curves with the same end points is always relative homotopy. Since the free homotopy classes correspond to conjugacy classes in the fundamental group, not elements, this convention fits better with homotopy classes. But since it's not really possible to put this precisely in the general case, I suggest changing it to a Don't get confused about section --Linus44 (talk) 20:36, 25 October 2012 (UTC)


 * Okay ... in the past there have been "Warning" sections, but that seems a little vague and all-encompassing. As we're trying to standardise on sections (trust me, L44, all this rigorous standardisation of format and structure has a purpose), I'd call the section "Danger of confusion" or "Source of possible confusion" or whatever. Others, thoughts? --prime mover (talk) 20:41, 25 October 2012 (UTC)


 * I didn't mean that literally; I intended to suggest something less definitive to avoid confusion. Shame the Bourbaki dangerous bend sign (can't believe this actually has an article) doesn't quite fit. --Linus44 (talk) 21:10, 25 October 2012 (UTC)