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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 29th 2018
   • (edited May 29th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexFurther in the spirit of uncovering (super-) homotopy-theoretic foundations for the theory of M-branes, we finally have a readable version of an article that spells out the mechanism of [[gauge enhancement]] on M-branes, via universal constructions in [[rational parameterized stable homotopy theory]] (as was previewed in the last part of my [talk](https://ncatlab.org/schreiber/show/StringMath2017) at StringMath17): * Hisham Sati, Vincent Braunack-Mayer, U.S.: _Gauge enhancement of Super M-Branes via rational parameterized stable homotopy theory_ ([web](https://ncatlab.org/schreiber/show/Gauge+enhancement+of+Super+M-Branes)) This applies, and was the original motivation for, the results from [Vincent Braunack-Mayer's PhD thesis](https://ncatlab.org/schreiber/show/thesis+Braunack-Mayer) on [[rational parameterized stable homotopy theory]]. While it's "just rational", it is not completely trivial, and we learn something about what the non-rational lift should look like. More on that another time...

   Further in the spirit of uncovering (super-) homotopy-theoretic foundations for the theory of M-branes, we finally have a readable version of an article that spells out the mechanism of gauge enhancement on M-branes, via universal constructions in rational parameterized stable homotopy theory (as was previewed in the last part of my talk at StringMath17):

   • Hisham Sati, Vincent Braunack-Mayer, U.S.:

     Gauge enhancement of Super M-Branes via rational parameterized stable homotopy theory

     (web)

   This applies, and was the original motivation for, the results from Vincent Braunack-Mayer’s PhD thesis on rational parameterized stable homotopy theory.

   While it’s “just rational”, it is not completely trivial, and we learn something about what the non-rational lift should look like. More on that another time…

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 30th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexOn page 5, when you write >The double dimensional reduction of these yields all the brane species in type IIA string theory, except the D6 and except the D8 followed by a figure illustrating this, the $D0$ is left all on its own, not arising from the fundamental branes in M-theory. Likewise the $F_2$ and the $\mu_{D0}$ later. For example, on the bottom of page 8, the $\mu_{D6}$ and $\mu_{D8}$ are highlighted as coming from the extra information arising from fibrewise stabilisation and cyclification, but not the $\mu_{D0}$. I know this is meant to come from something else, but it looks odd that the text doesn't connect with the figures. On p9 "The rational version of Snaith’s theorem is not a deep theorem but an immediate fact, as **?is** the rational version of its generalization from plain to twisted K-theory" (missing word?)

   On page 5, when you write

   The double dimensional reduction of these yields all the brane species in type IIA string theory, except the D6 and except the D8

   followed by a figure illustrating this, the $D0$ is left all on its own, not arising from the fundamental branes in M-theory. Likewise the $F_2$ and the $\mu_{D0}$ later. For example, on the bottom of page 8, the $\mu_{D6}$ and $\mu_{D8}$ are highlighted as coming from the extra information arising from fibrewise stabilisation and cyclification, but not the $\mu_{D0}$. I know this is meant to come from something else, but it looks odd that the text doesn’t connect with the figures.

   On p9 “The rational version of Snaith’s theorem is not a deep theorem but an immediate fact, as ?is the rational version of its generalization from plain to twisted K-theory” (missing word?)

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 30th 2018
   • (edited May 30th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the comment! True, the case of the D0 should be mentioned in the introduction. The new version now highlights this: The fundamental D0 is the incarnation of the circle fibration itself, in that its 2-form flux is really a form representative of the Chern class of the circle bundle. And yes, in that other sentence a word "is" was meant to be present. Thanks again.

   Thanks for the comment!

   True, the case of the D0 should be mentioned in the introduction. The new version now highlights this: The fundamental D0 is the incarnation of the circle fibration itself, in that its 2-form flux is really a form representative of the Chern class of the circle bundle.

   And yes, in that other sentence a word “is” was meant to be present. Thanks again.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 2nd 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexTypos: > M-therory; homotopty; equivalntly

   Typos:

   M-therory; homotopty; equivalntly

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 2nd 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! Fixed now.

   Thanks! Fixed now.