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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 28th 2013

have created an entry for Bott periodicity

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeAug 29th 2013

I haven’t thought about this for quite a long time, but I once had the following “dream”. Might it be possible to prove the Bott periodicity (say complex Bott periodicity, to keep things simple in the beginning), say in the form $K(X \times S^2) \cong K(X) \otimes K(S^2) = K(X)[\eta]/(\eta - 1)^2$, by calculating $K(S^2) \cong K(pt)[\eta]/(\eta - 1)^2$ constructively and interpreting that calculation in the topos of sheaves over $X$?