No abstract uploaded!

No abstract uploaded!

We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^ c case. In particular, we prove a K-theory version of the main results of [{\bf H}],[{\bf Liu1}, Theorem B] for a family of almost complex manifolds.

No abstract uploaded!

For projective conifold transitions between Calabi-Yau threefolds X and Y, with X close to Y in the moduli, we show that the combined information provided by the A model (Gromov–Witten theory in all genera) and B model (variation of Hodge structures) on X, linked along the vanishing cycles, determines the corresponding combined information on Y. Similar result holds in the reverse direction when linked with the exceptional curves.