3 papers
math.GR2024
Hurewicz and Dranishnikov-Smith theorems for asymptotic dimension of countable approximate groups
Tobias Hartnick, Vera Tonić
We establish two main results for the asymptotic dimension of countable approximate groups. The first one is a Hurewicz type formula for a global morphism of countable approximate…
math.GR2017
Bounded cohomology and virtually free hyperbolically embedded subgroups
Tobias Hartnick, Alessandro Sisto
Using a probabilistic argument we show that the second bounded cohomology of an acylindrically hyperbolic group (e.g., a non-elementary hyperbolic or relatively hyperbolic grou…
math.GR2014
On quasioutomorphism groups of free groups and their transitivity properties
Tobias Hartnick, Pascal Schweitzer
We introduce a notion of quasimorphism between two arbitrary groups, generalizing the classical notion of Ulam. We then define and study the category of homogeneous quasigroups, wh…