#### Volume 13, issue 4 (2013)

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Symplectic folding and nonisotopic polydisks

### Richard Hind

Algebraic & Geometric Topology 13 (2013) 2171–2192
##### Abstract

Let ${P}_{1}$ be a polydisk and ${P}_{2}=\varphi \left({P}_{1}\right)$ where $\varphi$ is a certain symplectic fold. We determine sharp lower bounds on the size of a ball containing the support of a symplectomorphism mapping ${P}_{1}$ to ${P}_{2}$. Optimal symplectomorphisms are the folds themselves. As a result, we construct symplectically nonisotopic polydisks in balls and in the complex projective plane.

##### Keywords
symplectic polydisk, Hamiltonian flow
##### Mathematical Subject Classification 2010
Primary: 53D35, 57R17
Secondary: 53D42