On the Lp-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky; Egor Shelukhin

doi:10.4310/MRL.2015.v22.n5.a1

On the L^p-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky, Egor Shelukhin

Department of Mathematics

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

10 Scopus citations

Abstract

We prove a number of results on the interrelation between the Lpmetric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily Lp-far from the subset A, answering a variant of a question of Polterovich for the Lp-metric.

Original language	English
Pages (from-to)	1275-1294
Number of pages	20
Journal	Mathematical Research Letters
Volume	22
Issue number	5
DOIs	https://doi.org/10.4310/MRL.2015.v22.n5.a1
State	Published - 1 Jan 2015

Keywords

Braid groups
Groups of Hamiltonian diffeomorphisms
L-metrics
Mapping class groups
Quasi-morphisms

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4310/MRL.2015.v22.n5.a1

Cite this

@article{a9958796e4224eaf9fa17027bd7db6f4,

title = "On the Lp-geometry of autonomous Hamiltonian diffeomorphisms of surfaces",

abstract = "We prove a number of results on the interrelation between the Lpmetric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily Lp-far from the subset A, answering a variant of a question of Polterovich for the Lp-metric.",

keywords = "Braid groups, Groups of Hamiltonian diffeomorphisms, L-metrics, Mapping class groups, Quasi-morphisms",

author = "Michael Brandenbursky and Egor Shelukhin",

year = "2015",

month = jan,

day = "1",

doi = "10.4310/MRL.2015.v22.n5.a1",

language = "English",

volume = "22",

pages = "1275--1294",

journal = "Mathematical Research Letters",

issn = "1073-2780",

publisher = "International Press of Boston, Inc.",

number = "5",

}

TY - JOUR

T1 - On the Lp-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

AU - Brandenbursky, Michael

AU - Shelukhin, Egor

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We prove a number of results on the interrelation between the Lpmetric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily Lp-far from the subset A, answering a variant of a question of Polterovich for the Lp-metric.

AB - We prove a number of results on the interrelation between the Lpmetric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily Lp-far from the subset A, answering a variant of a question of Polterovich for the Lp-metric.

KW - Braid groups

KW - Groups of Hamiltonian diffeomorphisms

KW - L-metrics

KW - Mapping class groups

KW - Quasi-morphisms

UR - http://www.scopus.com/inward/record.url?scp=84964994959&partnerID=8YFLogxK

U2 - 10.4310/MRL.2015.v22.n5.a1

DO - 10.4310/MRL.2015.v22.n5.a1

M3 - Article

AN - SCOPUS:84964994959

SN - 1073-2780

VL - 22

SP - 1275

EP - 1294

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 5

ER -