Dan Licata just told me a surprising (to me) fact that the homotopy groups of spheres are in fact known to be decidable! That is, there's an algorithm you can run that will tell you what group πkSn is --- but it's reeeeeeally slow. Like exponentially so.
Kenzo appears to contain an implementation of this algorithm, and has a lovely giant user manual written by some CS person who didn't even know any algebraic topology going in, which gives me hope it won't be too over the top with the intense math. I should probably check it out later.
Kenzo appears to contain an implementation of this algorithm, and has a lovely giant user manual written by some CS person who didn't even know any algebraic topology going in, which gives me hope it won't be too over the top with the intense math. I should probably check it out later.