There is classical description of cohomology ring of projective bundle. Is there an analog in quantum cohomology? 



Quantum cohomology of projective bundles
There is a quantum Leray-Hirsch Theorem, do to Maulik and Pandharipande [here](http://arxiv.org/abs/math/0412503). It relates the Gromov-Witten theory of the projective line bundle to that of the base.


