Journal of Symplectic Geometry
Volume 14 (2016)
Relative quasimorphisms and stably unbounded norms on the group of symplectomorphisms of the Euclidean spaces
Pages: 297 – 304
In the paper where Burago–Ivanov–Polterovich defined the notion of conjugation-invariant norms on groups, they asked whether there exists a group with stably bounded commutator length admitting stably unbounded norms. We show that the kernel of the Calabi homomorphism of the group of symplectomorphisms of the even-dimensional Euclidean space with compact support is such a group. To prove its stable unboundedness, we consider quasimorphisms relative to a conjugation-invariant norm.