Bounded cohomology of transformation groups

DOI10.1007/s00208-021-02266-8zbMath1490.57040arXiv1902.11067OpenAlexW3198828431MaRDI QIDQ2122064

Michael Brandenbursky, Michał Marcinkowski

Publication date: 5 April 2022

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.11067

zbMATH Keywords

homeomorphism groupsbounded cohomology

Mathematics Subject Classification ID

Geometric group theory (20F65) Cohomology of groups (20J06) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Connections of group theory with homological algebra and category theory (20J99) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Other homology theories in algebraic topology (55N35)

Related Items

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups, Norm-controlled cohomology of transformation groups, A short proof that the \(L^p\)-diameter of \(\mathrm{Diff}_0(S,\mathrm{area})\) is infinite

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the \(L^p\)-geometry of autonomous Hamiltonian diffeomorphisms of surfaces
• Characteristic classes of foliated surface bundles with area-preserving holonomy
• scl.
• Volume and bounded cohomology
• Characteristic classes in symplectic topology (with an appendix by Ludmil Katzarkov)
• The dimension of a cut locus on a smooth Riemannian manifold
• Continuous cohomology of the group of volume-preserving and symplectic diffeomorphisms, measurable transfer and higher asymptotic cycles
• Bounded cohomology and topologically tame Kleinian groups
• Signatures of foliated surface bundles and the symplectomorphism groups of surfaces
• Harmonic analysis, cohomology, and the large-scale geometry of amenable groups
• On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc
• On the moduli space of flat symplectic surface bundles
• Entropy and quasimorphisms
• Homological invariants and quasi-isometry.
• Deformations of spaces of imbeddings
• Acylindrically hyperbolic groups
• Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces
• Extending higher-dimensional quasi-cocycles
• Conjugation-invariant norms on groups of geometric origin
• Rozansky-Witten invariants via formal geometry
• On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus
• Fragmentation norm and relative quasimorphisms
• Commutators and diffeomorphisms of surfaces