Monotone Lagrangians in $\mathbb{C}{\mathbb{P}}^n$ of minimal Maslov number $n+1$

Abstract

We show that a monotone Lagrangian $L$ in $\mathbb{C}{\mathbb{P}}^n$ of minimal Maslov number $n+1$ is homeomorphic to a double quotient of a sphere, and thus homotopy equivalent to $\mathbb{R}{\mathbb{P}}^n$. To prove this we use Zapolsky’s canonical pearl complex for $L$ over $\mathbb{Z}$, 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 $\mathbb{C}{\mathbb{P}}^n$ on the resulting Floer homologies.

Momchil Konstantinov

ML Science/Engineering, Maths PhD