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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2012

    note on Bn-geometry

    • CommentRowNumber2.
    • CommentAuthorjim_stasheff
    • CommentTimeNov 27th 2012
    There's got to be better name!
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 27th 2012
    • (edited Nov 27th 2012)

    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 nB_n-geometry”, there needs to be an entry that says what is meant by this name.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 27th 2012

    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 nB_n series. I guess it’s not that.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 27th 2012
    • (edited Nov 27th 2012)

    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)SO(n,n) and hence of type D nD_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)SO(n+1,n), of type B nB_n.

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

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 27th 2012

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

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