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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2016

    I have started editing at Thom’s theorem. So far it has just the definition of the bordism ring, the statement of the theorem and some literature.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2016

    I have added a bunch of infrastructure (section Ingredients) and then spelled out in detail the proof (here) that the Pontrjagin-Thom construction first of all yields a well-defined function of sets

    {n-manifoldswithstablenormal-structure}π n(M). \left\{ {n\text{-}manifolds\;with\;stable} \atop {normal\;\mathcal{B}\text{-}structure} \right\} \longrightarrow \pi_n(M\mathcal{B}) \,.
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2016
    • (edited May 31st 2016)

    I have now spelled out the proof (here) that the PT construction yields a ring homomorphism Ω π (M)\Omega^\mathcal{B}_\bullet \to \pi_{\bullet}(M \mathcal{B}), and the idea of the proof (here) that this is an isomorphism.