On Two Remarkable Groups of Area-Preserving Homeomorphisms

Lev Buhovsky

doi:10.15407/mag19.02.339

On Two Remarkable Groups of Area-Preserving Homeomorphisms

Lev Buhovsky

Tel Aviv University, Weizmann Institute of Science

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

Abstract

We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and Müller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural Hofer pseudo-metric.

Original language	English
Pages (from-to)	339-373
Number of pages	35
Journal	Journal of Mathematical Physics, Analysis, Geometry
Volume	19
Issue number	2
DOIs	https://doi.org/10.15407/mag19.02.339
State	Published - 2023

Keywords

Fathi conjecture
Hamiltonian homeomorphisms
Hofer metric
spectral invariants

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

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10.15407/mag19.02.339

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title = "On Two Remarkable Groups of Area-Preserving Homeomorphisms",

abstract = "We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and M{\"u}ller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural Hofer pseudo-metric.",

keywords = "Fathi conjecture, Hamiltonian homeomorphisms, Hofer metric, spectral invariants",

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year = "2023",

doi = "10.15407/mag19.02.339",

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N2 - We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and Müller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural Hofer pseudo-metric.

AB - We prove that on a symplectic sphere, the group of Hamiltonian homeomorphisms in the sense of Oh and Müller is a proper normal subgroup of the group of finite energy Hamiltonian homeomorphisms. Moreover we detect infinite-dimensional flats inside the quotient of these groups endowed with the natural Hofer pseudo-metric.

KW - Fathi conjecture

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KW - Hofer metric

KW - spectral invariants

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U2 - 10.15407/mag19.02.339

DO - 10.15407/mag19.02.339

M3 - مقالة

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EP - 373

JO - Journal of Mathematical Physics, Analysis, Geometry

JF - Journal of Mathematical Physics, Analysis, Geometry

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On Two Remarkable Groups of Area-Preserving Homeomorphisms

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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