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 - 25 Mar 2023

Keywords

Fathi conjecture
Hamiltonian homeomorphisms
Hofer metric
spectral invariants

ASJC Scopus subject areas

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.",

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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.

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KW - Hofer metric

KW - spectral invariants

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DO - 10.15407/mag19.02.339

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JO - Journal of Mathematical Physics, Analysis, Geometry

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On Two Remarkable Groups of Area-Preserving Homeomorphisms

Abstract

Keywords

ASJC Scopus subject areas

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