Talk:Hopf invariant

Latest comment: 18 years ago by Ryan Reich in topic Thanks

I noticed this article was missing and gave a little exposition of the subject. If anyone would like to add relevant cross references, that'd be good. If you'd like any clarifications, let me know. - Thomas

Thanks

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Ooh, thanks for adding the references to those papers!

No problem. Ryan Reich 15:50, 27 March 2006 (UTC)Reply

Generalisations

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According to the article on the Hopf bundle, the construction can also be generalised to maps

 

by viewing   as a set of  -tuples   which are never all zero and mapping them to  . We can view   as a cell complex with one  -cell in dimension   for  , and we can attach a  -cell via   to obtain a new space  . This operation does not change the lower cohomology, and we get again one generator   and one generator  .

Would it make sense to define an invariant   such that  ?