 In the complex case one uses the complex dimension and the type is sometimes referred to as the complex type.While the type of a subbundle can in principle be any integer between 0 and 2"N", generalized almost complex structures cannot have a type greater than "N" because the sum of the subbundle and its complex conjugate must be all of formula_48

The type of a maximal isotropic subbundle is invariant under diffeomorphisms and also under shifts of the B-field, which are isometries of formula_1 of the form

where "B" is an arbitrary closed 2-form called the B-field in the string theory literature.The type of a generalized almost complex structure is in general not constant, it can jump by any even integer.