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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 15th 2009
   • PermaLink
   Author: Urs
   Format: Markdowncreated [[fivebrane 6-group]] with the idea

   created fivebrane 6-group with the idea

2. • CommentRowNumber2.
   • CommentAuthorGuest
   • CommentTimeJan 16th 2022
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   Author: Guest
   Format: TextIf one goes up the Whitehead tower starting from orthogonal group, one passes by the special orthogonal group, the spin group, the string 2-group before finally reaching the fivebrane 6-group. What comes after the fivebrane 6-group?

   If one goes up the Whitehead tower starting from orthogonal group, one passes by the special orthogonal group, the spin group, the string 2-group before finally reaching the fivebrane 6-group. What comes after the fivebrane 6-group?
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 16th 2022
   • (edited Jan 16th 2022)
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   Author: Urs
   Format: MarkdownItexBy dimensional reasons it's natural to speculate that killing the next non-torsion homotopy group gives "[[ninebrane structure]]" (Sati: [arXiv:1405.7686](https://arxiv.org/abs/1405.7686)). But there remains little known for sure on the physics side about the would-be nine-brane that one can compare the resulting structure to. To some extent this problem was already the case for the fivebrane structures. Just to note in this case that -- under "[[schreiber:Hypothesis H|Hypothesis H]]" -- we gave a rigorous proof that fivebrane structure cancels an M5-brane anomaly: see [Ex. 3.2](https://arxiv.org/pdf/1906.07417.pdf#page=11) and [Rem. 4.3](https://arxiv.org/pdf/1906.07417.pdf#page=18) in "[[schreiber:Twisted Cohomotopy implies M5 WZ term level quantization|Twisted Cohomotopy implies M5 WZ term level quantization]]". Since this discussion ultimately rests all on the quaternionic Hopf fibration $S^7 \to S^4$, it is natural to speculate that a variant based instead on the octonionic Hopf fibration $S^{15} \to S^7$ would give an analogous rigorous statement about 9-brane structure. But this would remain to be worked out.

   By dimensional reasons it’s natural to speculate that killing the next non-torsion homotopy group gives “ninebrane structure” (Sati: arXiv:1405.7686). But there remains little known for sure on the physics side about the would-be nine-brane that one can compare the resulting structure to.

   To some extent this problem was already the case for the fivebrane structures. Just to note in this case that – under “Hypothesis H” – we gave a rigorous proof that fivebrane structure cancels an M5-brane anomaly: see Ex. 3.2 and Rem. 4.3 in “Twisted Cohomotopy implies M5 WZ term level quantization”.

   Since this discussion ultimately rests all on the quaternionic Hopf fibration $S^7 \to S^4$, it is natural to speculate that a variant based instead on the octonionic Hopf fibration $S^{15} \to S^7$ would give an analogous rigorous statement about 9-brane structure. But this would remain to be worked out.

4. • CommentRowNumber4.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeJul 4th 2024
   • (edited Jul 4th 2024)
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   Author: Samuel Adrian Antz
   Format: MarkdownItexIs the title of [[fivebrane 6-group]] supposed to be small, when that of [[Fivebrane group]] is not? Edit: I just looked at the pages for [[ninebrane 10-group]] and [[ninebrane group]], where both titles are small. Edit: [[string 2-group]] and [[string group]] are also both small.

   Is the title of fivebrane 6-group supposed to be small, when that of Fivebrane group is not?

   Edit: I just looked at the pages for ninebrane 10-group and ninebrane group, where both titles are small.

   Edit: string 2-group and string group are also both small.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 4th 2024
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   Author: Urs
   Format: MarkdownItexnever made up my mind on this. The issue starts with "spin group". Let's agree on a convention and then try to harmonize the entry titles.

   never made up my mind on this. The issue starts with “spin group”.

   Let’s agree on a convention and then try to harmonize the entry titles.