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arXiv · 0802.0306

A Symplectic Isotopy of a Dehn Twist on CP^n x CP^{n+1}

Emiko Dupont
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Abstract

The complex manifold CP^n x CP^{n+1} with symplectic form σ_μ=σ_{CP^n}+μσ_{CP^{n+1}}, where σ_{CP^n} and σ_{CP^{n+1}} are normalized Fubini-Study forms, n a natural number and μ>1 a real number, contains a natural Lagrangian sphere L^μ. We prove that the Dehn twist along L^μ is symplectically isotopic to the identity for all μ>1. This isotopy can be chosen so that it pointwise fixes a complex hypersurface in CP^n x CP^{n+1} and lifts to the blow-up of CP^n x CP^{n+1} along a complex n-dimensional submanifold.

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Emiko Dupont. 2008-02-03. A Symplectic Isotopy of a Dehn Twist on CP^n x CP^{n+1}. https://doi.org/10.1112/jlms%2Fjdp020

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