Mathematical Proceedings of the Cambridge Philosophical Society

摘要

We show that a monotone Lagrangian L in CPn of minimal Maslov number n + 1 is homeomorphic to a double quotient of a sphere, and thus homotopy equivalent to RPn. To prove this we use Zapolsky's canonical pearl complex for L over Z, and twisted versions thereof, where the twisting is determined by connected covers of L. The main tool is the action of the quantum cohomology of CPn on the resulting Floer homologies.