..Hey everyone, this is my first post so please say something if it's in the wrong place or if I commit some faux pas :-)
So, the basic question is "Why does simple connectivity (in a topological sense; the fundamental group of some manifold M is trivial) imply there cannot be a finite covering of M?" The actual manifold we (my advisor and I) were discussing was CP^2, and she was trying to explain to me why were needed a branched covering. I'll deal with that later but right now I just need to understand this.
I guess I don't understand because I can think of things I would think are counter-examples: The closed disk should probably have a finite covering and it is simply connected. So any enlightenment would be great; I am new to topology but I really need to understand this stuff.
Thanks very much!