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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2011

    started Calabi-Yau object. But am being interrupted…

    • CommentRowNumber2.
    • CommentAuthorhilbertthm90
    • CommentTimeMay 28th 2011

    Is there a sense in which Calabi-Yau object is a generalization of Calabi-Yau manifold (for some definition…maybe trivial canonical bundle and some vanishing cohomology conditions)? I guess since this definition is for symmetric monoidal (infinity, 2)-categories, the question should be rephrased: is there a way to consider a Calabi-Yau manifold XX as an object in Bord 2\mathrm{Bord}_2 such that this is a Calabi-Yau object?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 29th 2011

    Right, that’s the natural next question.

    I am still in a rush and only had a handful of minutes. But as a start I have:

    Not much so far, but I give some pointers to the literature. Have to dash off now…

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2014

    ah, am just rediscovering this thread here, after over 3.5 years.

    The answer to #2 is of course: the A A_\infty-category of coherent sheaves on a smooth projective CY variety is a CY-A A_\infty-category. See here.