Symplectic folding and nonisotopic polydisks

Hind, Richard¹

¹Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, IN 46556, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2171-2192

Résumé

Let P1 be a polydisk and P2 = ϕ(P1) where ϕ is a certain symplectic fold. We determine sharp lower bounds on the size of a ball containing the support of a symplectomorphism mapping P1 to P2. Optimal symplectomorphisms are the folds themselves. As a result, we construct symplectically nonisotopic polydisks in balls and in the complex projective plane.

Détail

DOI : 10.2140/agt.2013.13.2171

Classification : 53D35, 57R17, 53D42
Keywords: symplectic polydisk, Hamiltonian flow

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