We find robust obstructions to representing a Hamiltonian diffeomorphism as a full k-th
power, k ≥ 2 k≥ 2, and in particular, to including it into a one-parameter subgroup. The …

Let $ S $ be a compact oriented surface. We construct homogeneous quasimorphisms on $
Diff (S, area) $, on $ Diff_0 (S, area) $ and on $ Ham (S) $ generalizing the constructions of …

We study bi-invariant word metrics on groups. We provide an efficient algorithm for
computing the bi-invariant word norm on a finitely generated free group and we construct an …

Let Σg be a closed orientable surface of genus g and let Diff 0 (Σg, area) be the identity
component of the group of area-preserving diffeomorphisms of Σg. In this paper, we present …

We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-
dimensional torus is unbounded. We provide examples of Hamiltonian diffeomorphisms with …

Let $ G $ be a group and $ N $ a normal subgroup of $ G $. We study the large scale
behavior, not the exact values themselves, of the stable mixed commutator length $ scl_ {G …

Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on
the group $\textrm {Diff} _\Omega^\infty (D^ 2,\partial D^ 2) $ of area-preserving …

In this monograph we lay the foundation for a theory of coarse groups and coarse actions.
Coarse groups are group objects in the category of coarse spaces, and can be thought of as …

Let Fn be the free group on n generators and g the surface group of genus g. We consider
two particular generating sets: the set of all primitive elements in Fn and the set of all simple …

We prove a number of results on the interrelation between the $ L^ p $-metric on the group
of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian …