Is there any good guide on covering space for idiots? Like a really dumped down approach to it . As I have an exam on this, but don't understand it and it's like 1/6th of the exam.
So I'm doing Hatcher problem and stuck on 4.
- Construct a simply-connected covering space of the space $X \subset \mathbb{R}^3$ that is a union of a sphere and diameter.
All I can think of is just connecting a bunch of spheres in a line.
But, yeah pretty scared will fail my degree because of this. So I need a good guide of covering spaces that isn't Hatcher. The only other uses heavy category theory which is even worse to read.
Best Answer
I think it will help if you "pull the diameter out of the sphere using the 4th dimension" (think about the analogous situation of a diameter in a circle) to see that space is homeomorphic to
Now this is similar to the wedge sum of a circle with a sphere which you might have seen before (I think there's a similar example in hatcher). If you want to see the solution to the problem, go here: http://i.imgur.com/afVPm.jpg