We prove the vanishing of bounded cohomology with separable dual coefficients for many
groups of interest in geometry, dynamics, and algebra. These include compactly supported …

In this paper, we give another proof of the result of Brandenbursky and Kȩdra which says
that the commutator subgroup of the infinite braid group admits stably unbounded norms …

A point in the (N, q)-torus knot in ℝ 3 goes q times along a vertical circle while this circle
rotates N times around the vertical axis. In the Lissajous-toric knot K (N, q, p), the point goes …

Bavard proved a duality theorem between commutator length and quasimorphisms. Burago,
Ivanov and Polterovich introduced the notion of a conjugation-invariant norm which is a …

We consider the symplectic representation $\rho_n $ of a braid group $ B (n) $ in $ Sp
(2l,\mathbb {Z}) $, for $ l=\Big [\dfrac {n-1}{2}\Big] $. If $ P $ is a $4 l^ 2$ polynomial on the …

We observe that a function on a group equipped with a bi-invariant word metric is Lipschitz if
and only if it is a partial quasimorphism bounded on the generating set. We also show that …

A point in the $(N, q) $-torus knot in $\mathbb {R}^ 3$ goes $ q $ times along a vertical circle
while this circle rotates $ N $ times around the vertical axis. In the Lissajous-toric knot $ K (N …

This thesis constructs unbounded quasimorphisms that are invariant under all
automorphisms on free products of groups and on graph products of finitely generated …

Abstract Let β:= σ 1 σ 2− 1 be a braid in B 3, where B 3 is the braid group on 3 strings and σ
1, σ 2 are the standard Artin generators. We use Gauss diagram formulas to show that for …