Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

D. Alvarez-Gavela; V. Kaminker; A. Kislev; K. Kliakhandler; A. Pavlichenko; L. Rigolli; D. Rosen; O. Shabtai; B. Stevenson; J. Zhang

doi:10.1142/S1793525319500213

Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

D. Alvarez-Gavela, V. Kaminker, A. Kislev, K. Kliakhandler, A. Pavlichenko, L. Rigolli, D. Rosen, O. Shabtai, B. Stevenson, J. Zhang

Research output: Contribution to journal › Article

Abstract

Given a symplectic surface (σ,ω) of genus g ≥ 4, we show that the free group with two generators embeds into every asymptotic cone of (Ham(σ,ω),d_H), where d_H is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

Original language	English (US)
Pages (from-to)	467-498
Number of pages	32
Journal	Journal of Topology and Analysis
Volume	11
Issue number	2
DOIs	https://doi.org/10.1142/S1793525319500213
State	Published - Jun 1 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

Hamiltonian diffeomorphisms
Hofer's metric
asymptotic cones
egg beater map
embeddings of free groups

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Cite this

Alvarez-Gavela, D., Kaminker, V., Kislev, A., Kliakhandler, K., Pavlichenko, A., Rigolli, L., Rosen, D., Shabtai, O., Stevenson, B., & Zhang, J. (2019). Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms. Journal of Topology and Analysis, 11(2), 467-498. https://doi.org/10.1142/S1793525319500213

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author = "D. Alvarez-Gavela and V. Kaminker and A. Kislev and K. Kliakhandler and A. Pavlichenko and L. Rigolli and D. Rosen and O. Shabtai and B. Stevenson and J. Zhang",

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AU - Alvarez-Gavela, D.

AU - Kaminker, V.

AU - Kislev, A.

AU - Kliakhandler, K.

AU - Pavlichenko, A.

AU - Rigolli, L.

AU - Rosen, D.

AU - Shabtai, O.

AU - Stevenson, B.

AU - Zhang, J.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Given a symplectic surface (σ,ω) of genus g ≥ 4, we show that the free group with two generators embeds into every asymptotic cone of (Ham(σ,ω),dH), where dH is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

AB - Given a symplectic surface (σ,ω) of genus g ≥ 4, we show that the free group with two generators embeds into every asymptotic cone of (Ham(σ,ω),dH), where dH is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

KW - Hamiltonian diffeomorphisms

KW - Hofer's metric

KW - asymptotic cones

KW - egg beater map

KW - embeddings of free groups

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