TITLE: Quantum cohomology of projective bundles
QUESTION [5 upvotes]: There is classical description of cohomology ring of projective bundle. Is there an analog in quantum cohomology?

REPLY [4 votes]: There is a quantum Leray-Hirsch Theorem, do to Maulik and Pandharipande here.  It relates the Gromov-Witten theory of the projective line bundle to that of the base.