# A Symplectic Isotopy of a Dehn Twist on CP^n x CP^{n 1} - Mathematics > Symplectic Geometry

A Symplectic Isotopy of a Dehn Twist on CP^n x CP^{n 1} - Mathematics > Symplectic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: The complex manifold CP^n x CP^{n+1} with symplectic form\sigma \mu=\sigma {CP^n}+\mu\sigma {CP^{n+1}}, where \sigma {CP^n} and\sigma {CP^{n+1}} are normalized Fubini-Study forms, n a natural number and\mu>1 a real number, contains a natural Lagrangian sphere L^{\mu}. We provethat the Dehn twist along L^{\mu} is symplectically isotopic to the identityfor all \mu>1. This isotopy can be chosen so that it pointwise fixes a complexhypersurface 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.

Author: ** Emiko Dupont**

Source: https://arxiv.org/