Pi4S3 Paper #1151
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Pi4S3 Paper #1151
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I think I proved it by pasting a lot of pushout diagrams. If there is a cubical flavored proof that's certainly better, though I might have relied on some judgmental equalities when further pasting the thing with other squares. It shouldn't be too much trouble to adjust though since squares are very modular. |
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Somehow agda took a lot longer checking one particular judgemental equality when I swapped the proof out. Should I be concerned? |
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@Trebor-Huang Hmm.. Maybe Agda is too keen on unfolding this definition or something? Could you point me to where in your code this happened? |
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This PR adds the formalisation behind
Formalising and computing the fourth homotopy group of the 3-sphere in Cubical Agda by me and @mortberg
I've had this stuff lying around for months but I forgot to make a PR... The primary addition is the
Cubical/Papers/Pi4S3-JournalVersion.agdawhich extendsCubical/Papers/Pi4S3.agda.There is some new maths but nothing that should be interfering. Most of it is in the new file
Cubical/HITs/Sn/Multiplication.agda. It contains theThere's also the equivalence between suspensions of smash products and joins (in
Cubical/HITs/Sn/SmashProduct/Base.agda.) which I saw was mentioned in Issue #1147 . I hope this doesn't cause any problems for @Trebor-Huang (please tell me in that case and we can probably change it back to your version).