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 › peer-review

2 Scopus citations

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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10.1142/S1793525319500213

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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),dH), where dH is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.",

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Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms. / Alvarez-Gavela, D.; Kaminker, V.; Kislev, A.; Kliakhandler, K.; Pavlichenko, A.; Rigolli, L.; Rosen, D.; Shabtai, O.; Stevenson, B.; Zhang, J.

In: Journal of Topology and Analysis, Vol. 11, No. 2, 01.06.2019, p. 467-498.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

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.

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KW - Hamiltonian diffeomorphisms

KW - Hofer's metric

KW - asymptotic cones

KW - egg beater map

KW - embeddings of free groups

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