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On Lagrangian embeddings into the complex projective spaces
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We prove that for any closed orientable connected [Formula: see text]-manifold [Formula: see text] and any Lagrangian immersion of the connected sum [Formula: see text] either into the complex projective [Formula: see text]-space [Formula: see text] or into the product [Formula: see text] of the complex projective line and the complex projective plane, there exists a Lagrangian embedding which is homotopic to the initial Lagrangian immersion. To prove this, we show that Eliashberg–Murphy’s [Formula: see text]-principle for Lagrangian embeddings with a concave Legendrian boundary and Ekholm–Eliashberg–Murphy–Smith’s [Formula: see text]-principle for self-transverse Lagrangian immersions with the minimal or near-minimal number of double points hold for six-dimensional simply connected compact symplectic manifolds.
Title: On Lagrangian embeddings into the complex projective spaces
Description:
We prove that for any closed orientable connected [Formula: see text]-manifold [Formula: see text] and any Lagrangian immersion of the connected sum [Formula: see text] either into the complex projective [Formula: see text]-space [Formula: see text] or into the product [Formula: see text] of the complex projective line and the complex projective plane, there exists a Lagrangian embedding which is homotopic to the initial Lagrangian immersion.
To prove this, we show that Eliashberg–Murphy’s [Formula: see text]-principle for Lagrangian embeddings with a concave Legendrian boundary and Ekholm–Eliashberg–Murphy–Smith’s [Formula: see text]-principle for self-transverse Lagrangian immersions with the minimal or near-minimal number of double points hold for six-dimensional simply connected compact symplectic manifolds.
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