Attending graduate school this Fall and need to understand fibrations better. I will be taking geometry and algebra. I've read a neat article Quanta Magazine Article on the topic of mirror worlds and symplectic spaces but I'd like to gain a deeper understanding of these concepts.
Consider $X=\Bbb R^2 / \{0\}.$
How do you fibrate $X$ by breaking up the space with hyperbola $y=k/x?$
I understand this basically for a sphere as our symplectic space, but not for the hyperbola. With a sphere you can just fibrate it into tori, then take the reciprocal of each tori and re-assemble to create another geometric shape.