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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 25th 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a little content. <a href="https://ncatlab.org/nlab/revision/diff/Seifert+surface/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seifert+surface/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Seifert+surface">current</a>

   Added a little content.

   diff, v3, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 25th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a warning that the notion of "Seifert surface" is un-related to that of "Seifert manifold" <a href="https://ncatlab.org/nlab/revision/diff/Seifert+surface/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seifert+surface/4">v4</a>, <a href="https://ncatlab.org/nlab/show/Seifert+surface">current</a>

   added a warning that the notion of “Seifert surface” is un-related to that of “Seifert manifold”

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 25th 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAccording to this entry, [EOM: Seifert matrix](https://encyclopediaofmath.org/wiki/Seifert_matrix), there are Seifert manifolds of all dimensions. Haven't checked, but it seems that Seifert surfaces are 2d Seifert manifolds.

   According to this entry, EOM: Seifert matrix, there are Seifert manifolds of all dimensions. Haven’t checked, but it seems that Seifert surfaces are 2d Seifert manifolds.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 25th 2024
   • (edited Nov 25th 2024)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexDuplicate

   Duplicate

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 25th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe full term for what is currently described at *[[Seifert manifold]]* is "Seifert fiber space" or "Seifert fibration" or the like: These are $S^1$-fibrations over a base space that may be an orbifold instead of a smooth manifold. So I think they are different concepts. But maybe for better disambiguation with the higher dimensional analog of Seifert surfaces (coboundaries of knots), we should rename that entry to "Seifert fibration" or something like this.

   The full term for what is currently described at Seifert manifold is “Seifert fiber space” or “Seifert fibration” or the like: These are $S^1$-fibrations over a base space that may be an orbifold instead of a smooth manifold.

   So I think they are different concepts.

   But maybe for better disambiguation with the higher dimensional analog of Seifert surfaces (coboundaries of knots), we should rename that entry to “Seifert fibration” or something like this.

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 25th 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexYes, it does seem different. EOM has [Seifert fibration](https://encyclopediaofmath.org/index.php?title=Seifert_fibration).

   Yes, it does seem different. EOM has Seifert fibration.

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 26th 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded something on the generalization to higher dimensions. <a href="https://ncatlab.org/nlab/revision/diff/Seifert+surface/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seifert+surface/6">v6</a>, <a href="https://ncatlab.org/nlab/show/Seifert+surface">current</a>

   Added something on the generalization to higher dimensions.

   diff, v6, current