Symplectic folding and nonisotopic polydisks

Let $P_{1}$ be a polydisk and $P_{2} = ϕ (P_{1})$ 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 $P_{1}$ 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.

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Keywords

symplectic polydisk, Hamiltonian flow

Mathematical Subject Classification 2010

Primary: 53D35, 57R17

Secondary: 53D42

References

Publication

Received: 31 October 2012

Revised: 4 February 2013

Accepted: 14 February 2013

Published: 6 June 2013

Authors

Richard Hind
Department of Mathematics University of Notre Dame 255 Hurley Notre Dame, IN 46556 USA
http://math.nd.edu/people/faculty/richard-k-hind/

Volume 13, issue 4 (2013)

Richard Hind

Abstract