Enlacements asymptotiques

Gambaudo, Jean-Marc; Ghys, Étienne

doi:10.1016/s0040-9383(97)00001-3

Cited by 61 publications

(92 citation statements)

References 3 publications

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“…In the particular case of area preserving maps of the 2-disk, only one of these invariant quantities is not trivial. In [5], it is shown that this invariant fits with our definition in the particular case when the invariant measures λ i are all equal to the area. …”

Section: The Calabi Invariant As a Minoration Of The Sequence (θ (1)supporting

confidence: 53%

Dynamical cocycles with values in the Artin braid group

Gambaudo¹,

Pécou

1999

Ergod. Th. Dynam. Sys.

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Section: The Calabi Invariant As a Minoration Of The Sequence (θ (1)supporting

confidence: 53%

Dynamical cocycles with values in the Artin braid group

Gambaudo¹,

Pécou

1999

Ergod. Th. Dynam. Sys.

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“…[20]. It turns out that the generalized Gambaudo-Ghys construction allows us to construct an infinite family of linearly independent Calabi quasi-morphisms, i.e.…”

Section: Letmentioning

confidence: 99%

Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

Brandenbursky

2015

Int. J. Math.

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Abstract. Let Σ g be a closed orientable surface of genus g and let Diff 0 (Σ g , area) be the identity component of the group of areapreserving diffeomorphisms of Σ g . In this work we present the extension of Gambaudo-Ghys construction to the case of a closed hyperbolic surface Σ g , i.e. we show that every non-trivial homogeneous quasi-morphism on the braid group on n strings of Σ g defines a non-trivial homogeneous quasi-morphism on the group Diff 0 (Σ g , area). As a consequence we give another proof of the fact that the space of homogeneous quasi-morphisms on Diff 0 (Σ g , area) is infinite dimensional.Let Ham(Σ g ) be the group of Hamiltonian diffeomorphisms of Σ g . As an application of the above construction we construct two injective homomorphisms Z m → Ham(Σ g ), which are bi-Lipschitz with respect to the word metric on Z m and the autonomous and fragmentation metrics on Ham(Σ g ). In addition, we construct a new infinite family of Calabi quasi-morphisms on Ham(Σ g ).

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“…Note that it is known (see, e.g., [5]) that the Calabi homomorphism does not behave continuously with respect to the C 0 -topology. For instance, one can consider the following example.…”

Section: Question 11 To Which Groups Of Homeomorphisms Does the Calmentioning

confidence: 99%

“…Let us also mention that Gambaudo and Ghys have proved that two diffeomorphisms of the disk that are conjugated by an area preserving homeomorphism have the same Calabi invariant [5]. Several non-trivial normal subgroups of Homeo c (D 2 , area) have been defined by Ghys [2], Oh-Muller [12] and recently by Le Roux [8].…”

Section: Remark 12mentioning

confidence: 99%