Symplectic topology of Lagrangian submanifolds of ?Pn with intermediate minimal Maslov numbers

摘要

We examine symplectic topological features of a certain family of monotone Lagrangian submanifolds in ?Pn. First we give cohomological constraints on a Lagrangian submanifold in ?Pn whose first integral homology is p-torsion. In the case where (n, p) = (5,3), (8, 3), we prove that the cohomologies with coefficients in ?2 of such Lagrangian submanifolds are isomorphic to that of SU(3)/(SO(3)?3) and SU(3)/?3, respectively. Then we calculate the Floer cohomology with coefficients in ?2 of a monotone Lagrangian submanifold SU(p)/?p in C P p 2 ? 1 .${mathbb C}P^{p^2-1}.$