Bounded cohomology and non-uniform perfection of mapping class groups

By H. Endo, D. Kotschick. 2000

67 citations recorded by the source corpus.

Abstract.Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus. This estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second bounded cohomology to ordinary cohomology is not injective.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d913a640b613497067ae237029d9c071ab6cd735

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quasi-morphisms on surface diffeomorphism groups (2019, background): “mov’s introduction of bounded cohomology in the early 80s [Gro82]. In the context of mapping class groups there are now many constructions of quasi-morphisms, starting with the work of Endo{Kotschick [EK01], Bestvina{ Fujiwara [BF02], and Hamenstadt [Ham08] to name only a few. Using the natural proj”
Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group (2014, background): “De plus, elle distingue (cid:128) des groupes modulaires des surfaces de type ﬁni, dont certains éléments ont une orbite bornée sur le complexe des courbes et une scl non nulle : en effet, Endo et Kotschick [13] et Korkmaz [21] ont montré que les twists de Dehn sont de scl strictement positive.”
Bounded cohomology of subgroups of mapping class groups (Hyperbolic Spaces and Discrete Groups) (2000, methodology): “Kotschick [5] have shown using 4-manifold topology and Seiberg-Witten invariants that Q̃H(MCG(S)) 6= 0 when S is hyperbolic.”