 For example,
On the formula_61-page the differential is
Higher odd-dimensional differentials formula_63 are given by Massey products for twisted K-theory tensored by formula_36.So
Note that if the underlying space is formal, meaning its rational homotopy type is determined by its rational cohomology, hence has vanishing Massey products, then the odd-dimensional differentials are zero.Pierre Deligne, Phillip Griffiths, John Morgan, and Dennis Sullivan proved this for all compact Kähler manifolds, hence formula_66 in this case.