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

Momchil Konstantinov; Jack Smith

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arXiv · 1810.00833

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

Momchil Konstantinov·Jack Smith

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Abstract

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

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BibTeX RIS

Momchil Konstantinov, Jack Smith. 2018-10-01. Monotone Lagrangians in $\mathbb{CP}^n$ of minimal Maslov number $n+1$. https://arxiv.org/abs/1810.00833

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