5 papers
Polynomial homological Dehn functions from non-proper actions
Roman Sauer, Jannis Weis
We establish a homological algebra framework for proving polynomiality of higher homological Dehn functions of groups. As an application, we show a combination theorem for polynomi…
An acylindrically hyperbolic group of non-uniform exponential growth
Roman Sauer, Eduard Schesler
We show the existence of an acylindrically hyperbolic group that has non-uniform exponential growth and Kazhdan's property . The group is constructed as a common quotient of a…
A finitely presented group of non-uniform exponential growth
Roman Sauer, Eduard Schesler
We provide the first example of a finitely presented, and the first example of a simple, group of non-uniform exponential growth. The example is given by Thompson's group V.
The algebraic cheap rebuilding property
Kevin Li, Clara Loeh, Marco Moraschini +2
We present an axiomatic approach to combination theorems for various homological properties of groups and, more generally, of chain complexes. Examples of such properties include a…
The cheap embedding principle: Dynamical upper bounds for homology growth
Kevin Li, Clara Loeh, Marco Moraschini +2
We provide upper bounds for logarithmic torsion homology growth and Betti number growth of groups, phrased in the language of measured group theory.