2019
DOI: 10.1142/s179352532050017x
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Disjoint superheavy subsets and fragmentation norms

Abstract: We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding I : R n → Ham(M ) with respect to the fragmentation norm on the group Ham(M ) of Hamiltonian diffeomorphisms of a symplectic manifold (M, ω). As an application, we provide an answer to Brandenbursky's question on fragmentation norms on Ham(Σg), where Σg is a closed Riemannian surface of genus g ≥ 2.

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Cited by 4 publications
(2 citation statements)
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“…To prove Lemma 3.1, we use the following lemma essentially proved in [MVZ,Theorem 1.3] and [KO,Lemma 3.17].…”
Section: Extension Of Quasimorphismmentioning
confidence: 99%
See 1 more Smart Citation
“…To prove Lemma 3.1, we use the following lemma essentially proved in [MVZ,Theorem 1.3] and [KO,Lemma 3.17].…”
Section: Extension Of Quasimorphismmentioning
confidence: 99%
“…The Calabi homomorphism is known to be well-defined and a group homomorphism (see [Cala], [Ban78], [Ban97] and [MS]). In terms of subadditive invariants, the Calabi property corresponds to the asymptotically vanishing spectrum condition in [KO,Definition 3.5]…”
Section: Applications To Symplectic Geometrymentioning
confidence: 99%