Monotone Lagrangians in of minimal Maslov number n + 1
Mathematical Proceedings of the Cambridge Philosophical Society(2020)
摘要
AbstractWe 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.
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