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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 4th 2013

some basics at spherical fibration

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 30th 2019

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeJun 19th 2019

Added something on the classifying space for spherical fibrations.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 19th 2019
• (edited Jun 19th 2019)

In more modern language and more generally, $F$-fiber infinity-bundles are classified by the delooping $B Aut(F)$ of the automorphism infinity-group of F. For $F =S^n$ this gives the classifying space for $n$-spherical fibrations.

The canonical inclusion $O(n+1) \hookrightarrow Aut(S^n)$ picks the subspace of twists coming from the J-,homomorphism.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeJun 20th 2019

Ok, we could update like that, but why were they using the H-spaces, $G_n$, that’s I guess what you call $Map(S^{n-1}, S^{n-1})$, rather than $Aut(S^n)$, the monoid rather than the group?