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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 6th 2014
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   Author: Urs
   Format: MarkdownItexI have added some minimum (or not even that) to _[[p-completion]]_. In the process I also created _[[analytic completion]]_ and gave _[[fracture theorem]]_ an Idea-section. (None of this is meant to be in the state in which it is, that's just how far I got in little available time...)

   I have added some minimum (or not even that) to p-completion. In the process I also created analytic completion and gave fracture theorem an Idea-section.

   (None of this is meant to be in the state in which it is, that’s just how far I got in little available time…)

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeApr 7th 2014
   • (edited Apr 7th 2014)
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   Author: Tim_Porter
   Format: MarkdownItexA useful reference for fracture theorems might be Dennis Sullivan: Genetics of Homotopy Theory and the Adams Conjecture, The Annals of Mathematics, Second Series, Vol. 100, No. 1 (Jul., 1974), pp. 1-79 or the MIT notes (which are linked from [[Dennis Sullivan]]). I found this much better motived than Bousfield-Kan, but am not sure it is quite on target for the entry.

   A useful reference for fracture theorems might be

   Dennis Sullivan:

   Genetics of Homotopy Theory and the Adams Conjecture, The Annals of Mathematics, Second Series, Vol. 100, No. 1 (Jul., 1974), pp. 1-79

   or the MIT notes (which are linked from Dennis Sullivan).

   I found this much better motived than Bousfield-Kan, but am not sure it is quite on target for the entry.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 7th 2014
   • (edited Apr 7th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks, I haven't looked at that yet. But just this minute I slightly expanded at _[[fracture theorem]]_ by adding a pointer to * Tilman Bauer, _Bousfield localization and the Hasse square_ ([pdf](http://math.mit.edu/conferences/talbot/2007/tmfproc/Chapter09/bauer.pdf)) which in section 2 attributes the arithmetic square for spectra to * Dennis Sullivan, _Geometric topology: localization, periodicity and Galois symmetry_, volume 8 of K- Monographs in Mathematics. Springer, Dordrecht, 2005. The 1970 MIT notes, Edited and with a preface by Andrew Ranicki. There is [this MO comment by Strickland](http://mathoverflow.net/a/91057/381) which attributes the modern general version to Hopkins.

   Thanks, I haven’t looked at that yet. But just this minute I slightly expanded at fracture theorem by adding a pointer to

   • Tilman Bauer, Bousfield localization and the Hasse square (pdf)

   which in section 2 attributes the arithmetic square for spectra to

   • Dennis Sullivan, Geometric topology: localization, periodicity and Galois symmetry, volume 8 of K- Monographs in Mathematics. Springer, Dordrecht, 2005. The 1970 MIT notes, Edited and with a preface by Andrew Ranicki.

   There is this MO comment by Strickland which attributes the modern general version to Hopkins.

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeApr 7th 2014
   • (edited Apr 7th 2014)
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   Author: Tim_Porter
   Format: MarkdownItexI think the recent importance of fracturing is for spectra, but Sullivan has some excellent things to say about the general problem. (I do not so much like his methods, but that is another thing.) Ranicki has an on line version of the notes.

   I think the recent importance of fracturing is for spectra, but Sullivan has some excellent things to say about the general problem. (I do not so much like his methods, but that is another thing.) Ranicki has an on line version of the notes.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 17th 2015
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   Author: Urs
   Format: MarkdownItexI see that in [Revision 9](https://ncatlab.org/nlab/revision/diff/p-completion/9) somebody had added a definition [here](https://ncatlab.org/nlab/revision/diff/p-completion/9#of_a_homotopy_type) which has the right idea, but mixes up some things, like inclusions/projections and limits/colimits. I am a bit short on time here, so for the moment I have just removed the edit. But of course eventually including the correct version would be desireable.

   I see that in Revision 9 somebody had added a definition here which has the right idea, but mixes up some things, like inclusions/projections and limits/colimits. I am a bit short on time here, so for the moment I have just removed the edit. But of course eventually including the correct version would be desireable.