A short proof that the \(L^p\)-diameter of \(\mathrm{Diff}_0(S,\mathrm{area})\) is infinite

DOI10.2140/agt.2023.23.883zbMath1527.58004arXiv2010.03000OpenAlexW3091836913MaRDI QIDQ6164245

Michał Marcinkowski

Publication date: 3 July 2023

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.03000

zbMATH Keywords

diffeomorphismbraid group\(L^p\) normmeasure-preserving diffeomorphismShnirelman conjecture

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05)

Cites Work

• Quasi-isometric embeddings into diffeomorphism groups
• On the \(L^p\)-geometry of autonomous Hamiltonian diffeomorphisms of surfaces
• Anti-trees and right-angled Artin subgroups of braid groups
• Generalized fluid flows, their approximation and applications
• On presentations of surface braid groups.
• Bounded cohomology of transformation groups
• The diameter of the symplectomorphism group is infinite
• The \(L^p\)-diameter of the group of area-preserving diffeomorphisms of \(S^2\)
• The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures
• QUASI-MORPHISMS AND L^p-METRICS ON GROUPS OF VOLUME-PRESERVING DIFFEOMORPHISMS
• Topological lower bounds on the distance between area preserving diffeomorphisms
• ON THE GEOMETRY OF THE GROUP OF DIFFEOMORPHISMS AND THE DYNAMICS OF AN IDEAL INCOMPRESSIBLE FLUID

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