Bounded cohomology and non-uniform perfection of mapping class groups

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.

to appear in Invent. Math

Cited by in corpus (24)

• Bounded cohomology of subgroups of mapping class groups
• Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire
• Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group
• The Birman-Hilden theory
• Signatures of foliated surface bundles and the symplectomorphism groups of surfaces
• Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality
• On cofinite subgroups of mapping class groups
• On stable commutator length in hyperelliptic mapping class groups
• Stable commutator length on mapping class groups
• Monodromy invariants in symplectic topology
• On the commutator length of a Dehn twist
• Failure of separation by quasi-homomorphisms in mapping class groups
• Bavard's duality theorem on conjugation-invariant norms
• Cosmetic crossing changes of fibered knots
• Signatures of surface bundles and stable commutator lengths of Dehn twists
• Lefschetz fibrations and Torelli groups
• Quasi-homomorphisms on mapping class groups vanishing on a handlebody group
• Stable commutator length of a Dehn twist
• The space of non-extendable quasimorphisms
• Minimal number of singular fibers in a nonorientable Lefschetz fibration
• On stable commutator lengths of Dehn twists along separating curves
• On the stabilisation height of fibre surfaces in $S^3$
• Every mapping class group is generated by 6 involutions
• On a question of Brendle and Benson