Relative quasimorphisms and stably unbounded norms on the group of symplectomorphisms of the Euclidean spaces

Concordance group and stable commutator length in braid groups

“…This answers an open problem from the paper by Burago, Ivanov and Polterovich [3]. Another example for the same problem has been recently provided by Kawasaki [7] who showed that the group of symplectic diffeomorphisms of the Euclidean space is stably unbounded.…”

Conjugation-invariant norms on the commutator subgroup of the infinite braid group

“…The definitions of (ν, p, q)-commutator length and ν-quasimorphisms are following. 4]). Let G be a group with a conjugation-invariant norm ν and p, q ∈ R >0 .…”

“…Brandenbursky and Kȩdra [1] proved the following theorem: Kawasaki [4] also showed that the commutator subgroup of Symp c (R 2n ) 0 is such a group, where Symp c (R 2n ) 0 is the group of symplectomorphisms with compact support isotopic to the identity of the standard symplectic space. In this paper, we give a proof of Theorem1.2 by using the idea of Kawasaki in [4]. Kawasaki introduced ν-quasimorphisms (or relative quasimorphisms) and the (ν, p, q)-commutator length cl ν,p,q .…”

Norm controlled cohomology of transformation groups

“…We note that the idea of the technique in Proposition 4.4 comes from the construction of relative quasimorphisms by Kawasaki [11] and Brandenbursky and Kȩdra [3]. Moreover, our construction also can be seen as a generalization of [3].…”