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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 4th 2013
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   Author: Urs
   Format: MarkdownItexsome basics at _[[spherical fibration]]_

   some basics at spherical fibration

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 30th 2019
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   Author: Urs
   Format: MarkdownItexadded pointer to * [[Raoul Bott]], [[Loring Tu]], Chapter 11 of _[[Differential Forms in Algebraic Topology]]_, Graduate Texts in Mathematics 82, Springer 1982 ([doi:10.1007/BFb0063500](https://doi.org/10.1007/BFb0063500)) <a href="https://ncatlab.org/nlab/revision/diff/spherical+fibration/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/spherical+fibration/9">v9</a>, <a href="https://ncatlab.org/nlab/show/spherical+fibration">current</a>

   added pointer to

   • Raoul Bott, Loring Tu, Chapter 11 of Differential Forms in Algebraic Topology, Graduate Texts in Mathematics 82, Springer 1982 (doi:10.1007/BFb0063500)

   diff, v9, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 19th 2019
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   Author: David_Corfield
   Format: MarkdownItexAdded something on the classifying space for spherical fibrations. <a href="https://ncatlab.org/nlab/revision/diff/spherical+fibration/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/spherical+fibration/10">v10</a>, <a href="https://ncatlab.org/nlab/show/spherical+fibration">current</a>

   Added something on the classifying space for spherical fibrations.

   diff, v10, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 19th 2019
   • (edited Jun 19th 2019)
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   Author: Urs
   Format: MarkdownItexIn 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]].

   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.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 20th 2019
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   Author: David_Corfield
   Format: MarkdownItexOk, 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?

   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?