Can anyone familiar with this theorem and its proof let me know how much algebraic topology is involved, and where specifically? I am familiar with a lot of differential geometry, but not many of the algebraic aspects like cohomology, Lie groups, etc. From the ground up could you make it through sphere theorem without any of these tools?
Assuming algebra is required somewhere along the way, would it be more in the way of basic machinery, or in more sophisticated, deep results?
Thanks a lot!