27 citations · 116 across the 31 of their papers we have counts for
26 papers · 1 filter
Elementwise conservative actions and new constructions of boomerang subgroups
Yair Glasner, Tobias Hartnick, Waltraud Lederle
We show that countable non-abelian free groups admit uncountably many mutually singular elementwise conservative non-singular random subgroups, which are supported on infinite subg…
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…
Automorphism groups of cocompact CAT(0) cube complexes and simplicity
Tobias Hartnick, Merlin Incerti-Medici
We provide a systematic description of the automorphism groups of specially cocompact CAT(0) cube complexes. We show that these groups are topologically finitely generated, present…
Automorphisms of self-similar trees
Tobias Hartnick, Merlin Incerti-Medici
We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit o…
A Quillen Stability Criterion for Bounded Cohomology
Carlos De la Cruz Mengual, Tobias Hartnick
We provide a version of Quillen's homological stability criterion for continuous bounded cohomology. This criterion is exploited in the companion paper (arXiv:2201.03879) in order…
Higher finiteness properties of arithmetic approximate lattices: The Rank Theorem for number fields
Tobias Hartnick, Stefan Witzel
We introduce geometric and homological finiteness properties for countable approximate groups via coarse geometry and then study these finiteness properties for S-arithmetic reduct…
Stabilization of Bounded Cohomology for Classical Groups
Carlos De la Cruz Mengual, Tobias Hartnick
We show that bounded cohomology stabilizes along sequences of classical Lie groups, and along sequences of lattices in them. Our method is based on a criterion from (arXiv:2307.128…
Efficient computations with counting functions on free groups and free monoids
Tobias Hartnick, Alexey Talambutsa
We present efficient algorithms to decide whether two given counting functions on non-abelian free groups or monoids are at bounded distance from each other and to decide whether t…
Foundations of geometric approximate group theory
Matthew Cordes, Tobias Hartnick, Vera Tonić
We develop the foundations of a geometric theory of countably-infinite approximate groups, extending work of Björklund and the second-named author. Our theory is based on the notio…
Borel density for approximate lattices
Michael Björklund, Tobias Hartnick, Thierry Stulemeijer
We extend classical density theorems of Borel and Dani--Shalom on lattices in semisimple, respectively solvable algebraic groups over local fields to approximate lattices. Our proo…
Stability in Bounded Cohomology for Classical Groups, I: The Symplectic Case
Carlos De la Cruz Mengual, Tobias Hartnick
We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along…
Analytic properties of approximate lattices
Michael Björklund, Tobias Hartnick
We introduce a notion of cocycle-induction for strong uniform approximate lattices in locally compact second countable groups and use it to relate (relative) Kazhdan- and Haagerup-…
Kac-Moody symmetric spaces
Walter Freyn, Tobias Hartnick, Max Horn +1
In the present article we introduce and study a class of topological reflection spaces that we call Kac-Moody symmetric spaces. These generalize Riemannian symmetric spaces of non-…
Approximate lattices
Michael Björklund, Tobias Hartnick
In this article we introduce and study uniform and non-uniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense…
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…
Relations between counting functions on free groups and free monoids
Tobias Hartnick, Alexey Talambutsa
We consider finite sums of counting functions on the free group and the free monoid for . Two such sums are considered equivalent if they differ by a bounded…
Quasi-state Rigidity for Finite-dimensional Lie Algebras
Michael Björklund, Tobias Hartnick
We say that a Lie algebra $\gfr$ is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending…
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…
Bounded cohomology via partial differential equations, I
Tobias Hartnick, Andreas Ott
We present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an applica…
On topological twin buildings and topological split Kac-Moody groups
Tobias Hartnick, Ralf Köhl, Andreas Mars
We prove that a two-spherical split Kac-Moody group over a local field naturally provides a topological twin building in the sense of Kramer. This existence result and the local-to…
Weakly maximal representations of surface groups
Gabi Ben Simon, Marc Burger, Tobias Hartnick +2
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invar…
Quasi-Total Orders and Translation Numbers
Gabi Ben Simon, Tobias Hartnick
We show that a group admits a non-zero homogeneous quasimorphism if and only if it admits a certain type of action on a poset. Our proof is based on a construction of quasimorphism…
Invariant Orders on Hermitian Lie Groups
Gabi Ben Simon, Tobias Hartnick
We study three natural bi-invariant partial orders on a certain covering group of the automorphism group of a bounded symmetric domain of tube type; these orderings are defined usi…
Biharmonic functions on groups and limit theorems for quasimorphisms along random walks
Michael Björklund, Tobias Hartnick
We show for very general classes of measures on locally compact second countable groups that every Borel measurable quasimorphism is at bounded distance from a quasi-biharmonic one…