# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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

$\left\{ {n\text{-}manifolds\;with\;stable} \atop {normal\;\mathcal{B}\text{-}structure} \right\} \longrightarrow \pi_n(M\mathcal{B}) \,.$
• 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 $\Omega^\mathcal{B}_\bullet \to \pi_{\bullet}(M \mathcal{B})$, and the idea of the proof (here) that this is an isomorphism.