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arXiv · 1606.01964

Heavy subsets and non-contractible trajectories

Morimichi Kawasaki
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Abstract

Entov and Polterovich defined heaviness for closed subsets of a symplectic manifold by using the Hamiltonian Floer theory on contractible trajectories. Heavy subsets are known to be non-displaceable. In the present paper, we define a relative symplectic capacity $C(M,X,R;e)$ for a symplectic manifold $(M,\omega)$ and its subset $X$ which measures the existence of non-contractible trajectories of Hamiltonian isotopies on the product with annulus. We prove that $C(M,X,R;e)$ is finite if $(M,\omega)$ is monotone and $X$ is a heavy subset. We also prove that $C(M,X,R;e)$ is infinite if $X$ is a displaceable compact subset.

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Morimichi Kawasaki. 2016-06-06. Heavy subsets and non-contractible trajectories. https://arxiv.org/abs/1606.01964

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