The biran decomposition: A symplectic lefshetz hyperplane theorem
The biran decomposition: A symplectic lefshetz hyperplane theorem
Summary:
The symplectic structure of a Kahler manifold decomposes into two pieces: A symplectic disc bundle over a hyperplane section, and an isotropic skeleton. This Biran decomposition is a symplectic refinement of the Lefshetz hyperplane theorem. The proof uses the morse theory of the norm squared of a holomorphic section of the prequantum line bundle. We will use this to prove some lagrangian barrier phemonena. For example, every symplectic ball of radius $1/\sqrt{2}$ embedded in $\mathbb{C} \mathbb{P}^n$ interesects $\mathbb{R} \mathbb{P}^n$
Presented at:
- Student symplectic seminar
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