Article contents
Monotone Lagrangians in
${\mathbb{C}}{\mathbb{P}}^n$ of minimal Maslov number n + 1
Published online by Cambridge University Press: 21 February 2020
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.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 171 , Issue 1 , July 2021 , pp. 1 - 21
- Copyright
- © Cambridge Philosophical Society 2020
References
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