Proof of the main conjecture on $g$-areas

François Lalonde; Egor  Shelukhin

doi:10.3934/era.2015.22.92

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2015, Volume 22: 92-102. Doi: 10.3934/era.2015.22.92

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Proof of the main conjecture on $g$-areas

François Lalonde^1, and
Egor Shelukhin^2,

1.
Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal H3C 3J7, Québec
2.
Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal H3C 3J7, Québec

Received: May 31, 2015

Revised: July 31, 2015

Published: January 2015

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Abstract

In this paper, we prove the main conjecture on $g$-areas arising from [7]. That conjecture was announced by the first author in 2004. It~states that the $g$-area of any Hamiltonian diffeomorphism $\phi$ is equal to the positive Hofer pseudo-distance between $\phi$ and the subspace of Hamiltonian diffeomorphisms that can be expressed as a product of at most $g$ commutators.

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Mathematics Subject Classification: 53C15, 53D22, 53D40, 53D45, 57R58, 57S05, 58B20.

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References

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