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1. • CommentRowNumber1.
   • CommentAuthorGuest
   • CommentTimeNov 12th 2009
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   Author: Guest
   Format: TextCreated [[Dold fibration]]

   Created Dold fibration
2. • CommentRowNumber2.
   • CommentAuthorAndrew Stacey
   • CommentTimeNov 12th 2009
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   Author: Andrew Stacey
   Format: MarkdownYou are David Roberts and I claim my 5 pounds! (At least, if you aren't then someone's impersonating you on the n-lab)

   You are David Roberts and I claim my 5 pounds!

   (At least, if you aren't then someone's impersonating you on the n-lab)

3. • CommentRowNumber3.
   • CommentAuthorAndrew Stacey
   • CommentTimeNov 12th 2009
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   Author: Andrew Stacey
   Format: MarkdownTo make up for my frivolity, here's a serious question: is a "Dold fibration" the same thing as a quasi-fibration?

   To make up for my frivolity, here's a serious question: is a "Dold fibration" the same thing as a quasi-fibration?

4. • CommentRowNumber4.
   • CommentAuthorGuest
   • CommentTimeNov 12th 2009
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   Author: Guest
   Format: TextNext time I'm in Norway... A quasifibration is different - it is characterised by the property that the canonical maps from each fibre to the corresponding homotopy fibre are all weak homotopy equivalences. I've forgotten if Dold fibrations and quasifibrations are comparable, but looking at the 1958 article by Dold and Thom where quasifibrations are introduced, one gets a long exact sequence in homotopy for those as well. There was a bit of to and fro on the Hopf mailing list in 2001 on this, I should get a more complete transcript than what I have on my hard drive and extract some useful points. My gut feeling is that quasifibration is a weaker notion, and it looks tempting to guess that Dold fibrations are quasifibrations. But it is late here, and I'm not going to commit myself. -David Roberts

   Next time I'm in Norway...
   
   A quasifibration is different - it is characterised by the property that the canonical maps from each fibre to the corresponding homotopy fibre are all weak homotopy equivalences. I've forgotten if Dold fibrations and quasifibrations are comparable, but looking at the 1958 article by Dold and Thom where quasifibrations are introduced, one gets a long exact sequence in homotopy for those as well. There was a bit of to and fro on the Hopf mailing list in 2001 on this, I should get a more complete transcript than what I have on my hard drive and extract some useful points.
   
   My gut feeling is that quasifibration is a weaker notion, and it looks tempting to guess that Dold fibrations are quasifibrations. But it is late here, and I'm not going to commit myself.
   
   -David Roberts
5. • CommentRowNumber5.
   • CommentAuthorGuest
   • CommentTimeNov 12th 2009
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   Author: Guest
   Format: TextAdded comment to bottom of [[Dold fibration]] about quasifibrations, re previous post. David Roberts

   Added comment to bottom of Dold fibration about quasifibrations, re previous post.
   
   David Roberts
6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 12th 2009
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   Author: Urs
   Format: MarkdownYou know that it is forbidden (by me, if that matters) to have a useful technical exchange here? If anyone asks a good question here, like Andrew above, the only allowed answers are a) it's already on the nLab. See xyz or b) I have just typed the answer into this nLab entry: xyz .

   You know that it is forbidden (by me, if that matters) to have a useful technical exchange here?

   If anyone asks a good question here, like Andrew above, the only allowed answers are

   a) it's already on the nLab. See xyz

   or

   b) I have just typed the answer into this nLab entry: xyz .

7. • CommentRowNumber7.
   • CommentAuthorGuest
   • CommentTimeNov 12th 2009
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   Author: Guest
   Format: TextMy apologies - I was not aware of that. I will get around to putting the relevant info at [[quasifibration]] and [[Dold fibration]] soon. David Roberts

   My apologies - I was not aware of that. I will get around to putting the relevant info at quasifibration and Dold fibration soon.
   
   David Roberts
8. • CommentRowNumber8.
   • CommentAuthorAndrew Stacey
   • CommentTimeNov 13th 2009
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   Author: Andrew Stacey
   Format: Markdown@David: I hope you are aware that Urs was quasi-joking. Also, Urs' remark was more aimed at me since I should have put a query box at the n-lab and said "Query at [[Dold fibration]] about relationship to quasi-fibrations". Apologies to you both: to Urs for not remembering the Rules, to David for leading you astray!

   @David: I hope you are aware that Urs was quasi-joking. Also, Urs' remark was more aimed at me since I should have put a query box at the n-lab and said "Query at Dold fibration about relationship to quasi-fibrations".

   Apologies to you both: to Urs for not remembering the Rules, to David for leading you astray!

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeNov 13th 2009
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   Author: Urs
   Format: MarkdownYes, I was joking. But I took it David stayed within the role I jokingly assigned to him? Maybe not. Text-mode humour is difficult. All I mean to say from time to time is: let's not forget to put material on the nLab! :-)

   Yes, I was joking. But I took it David stayed within the role I jokingly assigned to him? Maybe not. Text-mode humour is difficult.

   All I mean to say from time to time is: let's not forget to put material on the nLab! :-)

10. • CommentRowNumber10.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 30th 2025
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    Author: DavidRoberts
    Format: MarkdownItexReplaced a really old query box of mine with a link to the actual MO question I asked, with the counterexamples. Someone with spare time and energy can import the example description to the nLab page, I hope. --- There is another query box that I am moving to here: +--{: .query} [[Chris Schommer-Pries]]: I believe this is an example of a quasi-fibration which is not a Serre fibration, but it is not a Dold fibration either. =-- which was attached to the construction > Here is a very simple counter-example due to Dold. Consider the union of line segments $$ E:= [-1,0]\times\{2\} \cup \{0\}\times [1,2] \cup [0,1]\times\{1\} $$ in $\mathbf{R}^2$, and the map projecting on to the first coordinate, $pr_1:E \to [-1,1]$. Then this map is a Dold fibration but not a Serre fibration. that showed the claim that not all Dold fibrations are Serre fibrations. <a href="https://ncatlab.org/nlab/revision/diff/Dold+fibration/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/Dold+fibration/15">v15</a>, <a href="https://ncatlab.org/nlab/show/Dold+fibration">current</a>

    Replaced a really old query box of mine with a link to the actual MO question I asked, with the counterexamples. Someone with spare time and energy can import the example description to the nLab page, I hope.

    ---

    There is another query box that I am moving to here:

    +–{: .query} Chris Schommer-Pries: I believe this is an example of a quasi-fibration which is not a Serre fibration, but it is not a Dold fibration either. =–

    which was attached to the construction

    Here is a very simple counter-example due to Dold. Consider the union of line segments

    in , and the map projecting on to the first coordinate, . Then this map is a Dold fibration but not a Serre fibration.

    that showed the claim that not all Dold fibrations are Serre fibrations.

    diff, v15, current