  We prove that the Gromov--Witten theory (GWT) of a projective bundle can be
determined by the Chern classes and the GWT of the base. It completely answers
a question raised in a previous paper (arXiv:1607.00740). Its consequences
include that the GWT of the blow-up of X at a smooth subvariety Z is uniquely
determined by GWT of X, Z plus some topological data.
