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Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms
Journal article   Peer reviewed

Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

D. Alvarez-Gavela, Kaminker, A. Kislev, K. Kliakhandler, A. Pavlichenko, L. Rigolli, D. Rosen, O. Shabtai, B. Stevenson and J. Zhang
Journal of topology and analysis, Vol.11(2), pp.467-498
06/01/2019
DOI: https://doi.org/10.1142/S1793525319500213

Abstract

Science & Technology Mathematics Physical Sciences
Given a symplectic surface (Sigma, omega) of genus g >= 4, we show that the free group with two generators embeds into every asymptotic cone of (Ham(Sigma, omega), d(H)), where d(H) is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

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