Talk:Fundamental group

Here's a very rough version of a rewrite of this article. What do you think about the level and scope? In many places I've gotten verbose by trying to keep an appeal to intuition going. Should I write out more things in symbols, or just try to sharpen the exposition? Jump in and help out!

A few things which I've been sloppy about and will try to fix up:

• Why we need a basepoint (and I often ignore it later).
• In writing intuition, pay attention to the words path vs. loop vs. class of loops.
• Discussion of SvK theorem is a bit useless for now.
• It would be nice to have an example of a space with finite fundamental group, or at least an element of finite order. <math>\mathbb R \mathbb P^2</math> is the obvious candidate since there's any easy geometric description of such an element, but that would probably merit a page of its own.
• Need pictures!

--MarkGall 01:21, 4 July 2009 (EDT)

Great work, but I'd like to improve the introductory definition to make it more understandable. Also, the group structure equation is broken towards the end. But your start on this is superb, and a fine place upon which to build.--Andy Schlafly 13:38, 4 July 2009 (EDT)

I agree about the introduction. I'm trying to think of a better way to motivate it, by talking about distinguishing spaces by looking at holes in them or something along those lines. Whoops, didn't notice the broken equations. The error is that PNG didn't convert right. I'm pretty sure they're correct latex -- anyone know the adjustments that are necessary to get this on-wiki? Do I need to use an array instead of the cases environment? --MarkGall 13:46, 4 July 2009 (EDT)