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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 26th 2012
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   Author: Urs
   Format: MarkdownItexnote on _[[Bn-geometry]]_

   note on Bn-geometry

2. • CommentRowNumber2.
   • CommentAuthorjim_stasheff
   • CommentTimeNov 27th 2012
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   Author: jim_stasheff
   Format: TextThere's got to be better name!

   There's got to be better name!
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 27th 2012
   • (edited Nov 27th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexActually, the developments show that there need not be a new name at all, as this is just part of T-duality, as is kown now. But since people still refer to it as "$B_n$-geometry", there needs to be an entry that says what is meant by this name.

   Actually, the developments show that there need not be a new name at all, as this is just part of T-duality, as is kown now. But since people still refer to it as “$B_n$-geometry”, there needs to be an entry that says what is meant by this name.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeNov 27th 2012
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   Author: Todd_Trimble
   Format: MarkdownItexOf course you can't help that it's called that, but I agree it's not a great name. My first association would be an incidence geometry modeled on a Coxeter group in the $B_n$ series. I guess it's *not* that.

   Of course you can’t help that it’s called that, but I agree it’s not a great name. My first association would be an incidence geometry modeled on a Coxeter group in the $B_n$ series. I guess it’s not that.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 27th 2012
   • (edited Nov 27th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexActually it is. Plain [[generalized complex geometry]] is controled by the structure group of the [[generalized tangent bundle]] of a manifold, which is $SO(n,n)$ and hence of type $D_n$. Here now one adds a line bundle to this (the Poincare line bundle of the T-duality correspondence) and so the structure group becomes $SO(n+1,n)$, of type $B_n$. I have added a brief note to this extent to the entry.

   Actually it is. Plain generalized complex geometry is controled by the structure group of the generalized tangent bundle of a manifold, which is $SO(n,n)$ and hence of type $D_n$. Here now one adds a line bundle to this (the Poincare line bundle of the T-duality correspondence) and so the structure group becomes $SO(n+1,n)$, of type $B_n$.

   I have added a brief note to this extent to the entry.

6. • CommentRowNumber6.
   • CommentAuthorTodd_Trimble
   • CommentTimeNov 27th 2012
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   Author: Todd_Trimble
   Format: MarkdownItexOh, thanks! So it *is* a good name after all.

   Oh, thanks! So it is a good name after all.