# A coarse embedding theorem for homological filling functions

@article{Kropholler2020ACE, title={A coarse embedding theorem for homological filling functions}, author={Robert P. Kropholler and Mark Pengitore}, journal={arXiv: Geometric Topology}, year={2020} }

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a coarse embeddings into hyperbolic group of geometric dimension $2$, characterizations of finitely presentable subgroups of groups with quadratic Dehn function with geometric dimension $2$, and to coarse embeddings of nilpotent groups into other nilpotent… Expand

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Superexponential Dehn functions inside CAT(0) groups

- Mathematics
- 2021

We construct 4–dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp(x) for integers n,m ≥ 1 and 6–dimensional CAT(0) groups containing finitely presented… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES

Groups with no coarse embeddings into hyperbolic groups

- Mathematics
- 2017

We introduce an obstruction to the existence of a coarse embedding of a given group or space into a hyperbolic group, or more generally into a hyperbolic graph of bounded degree. The condition we… Expand

Bounded cohomology characterizes hyperbolic groups

- Mathematics
- 2002

A finitely presentable group G is hyperbolic if and only if the map H 2 b (G, V ) → H 2 (G, V ) is surjective for any bounded G-module. The ‘only if’ direction is known and here we prove the ‘if’… Expand

A Subgroup Theorem for Homological Filling Functions

- Mathematics
- 2014

We use algebraic techniques to study homological filling functions of groups and their subgroups. If $G$ is a group admitting a finite $(n+1)$--dimensional $K(G,1)$ and $H \leq G$ is of type… Expand

Analysis and Geometry on Groups

- Mathematics
- 1993

Preface Foreword 1. Introduction 2. Dimensional inequalities for semigroups of operators on the Lp spaces 3. Systems of vector fields satisfying Hormander's condition 4. The heat kernel on nilpotent… Expand

Translation-like actions of nilpotent groups

- Mathematics
- Journal of Topology and Analysis
- 2019

We give a new obstruction to translation-like actions on nilpotent groups. Suppose we are given two finitely generated torsion-free nilpotent groups with the same degree of polynomial growth, but… Expand

Subgroups of Word Hyperbolic Groups in Dimension 2

- Mathematics
- 1996

If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 and it is… Expand

Filling invariants of stratified nilpotent Lie groups

- Mathematics
- Mathematische Zeitschrift
- 2018

Filling invariants are measurements of a metric space describing the behaviour of isoperimetric inequalities. In this article we examine filling functions and higher divergence functions. We prove… Expand

Homological Invariants and Quasi-Isometry

- Mathematics
- 2003

Abstract.Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain that… Expand

The Dehn function of SL(n;Z)

- Mathematics
- 2009

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z)… Expand

Homological and homotopical higher-order filling functions

- Mathematics
- 2008

We construct groups in which FV^3(n) != \delta^2(n). This construction also leads to groups G_k, k >= 3 for which \delta^{k}(n) is not subrecursive.