Dawid Kielak

activity

20112025

most citedResidually finite rationally solvable groups and virtual fibring

38 citations · 139 across the 31 of their papers we have counts for

collaborators

35 papers

math.GR2025

Virtual fibring of manifolds and groups

Dawid Kielak

The topic of this survey is the phenomenon of fibring over the circle for manifolds, and its group-theoretic twin, algebraic fibring. We will discuss the state of the art, and expl…

math.GR2025

Virtual fibring of Poincaré-duality groups

Sam P. Fisher, Giovanni Italiano, Dawid Kielak

We show that a RFRS Poincaré-duality group $G$ admits a virtual epimorphism to the integers whose kernel is itself a Poincaré-duality group over every field if and only if the $L^2…

math.GR2024

Non-vanishing unitary cohomology of low-rank integral special linear groups

Benjamin Brück, Sam Hughes, Dawid Kielak +1

We construct explicit finite-dimensional orthogonal representations $π_{N}$ of $SL_{N} (Z)$ for $N \in {3, 4}$ all of whose invariant vectors are trivial, and…

math.GT2024

BNSR invariants and $ℓ^{2}$ -homology

Sam Hughes, Dawid Kielak

We prove that if the $n$ th $ℓ^{2}$ -Betti number of a group is non-zero then its $n$ th BNSR invariant over $Q$ is empty, under suitable finiteness conditions. We apply thi…

math.GT2023

Coboundary expansion and Gromov hyperbolicity

Dawid Kielak, Piotr W. Nowak

We prove that if a compact $n$ -manifold admits a sequence of residual covers that form a coboundary expander in dimension $n - 2$ , then the manifold has Gromov-hyperbolic fundamental…

math.GT2023

Stallings's Fibring Theorem and $PD^{3}$ -pairs

Martin R. Bridson, Dawid Kielak, Monika Kudlinska

We give a relatively self-contained proof that if a group $G$ fibres algebraically and is part of a $PD^{3}$ -pair, then $G$ is the fundamental group of a fibred compact asph…

math.GR2023

Kazhdan constants for Chevalley groups over the integers

Marek Kaluba, Dawid Kielak

We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than $A_{n}$ , these ar…

math.GT2023

Group rings of three-manifold groups

Dawid Kielak, Marco Linton

Let $G$ be the fundamental group of a three-manifold. By piecing together many known facts about three manifold groups, we establish two properties of the group ring $C G$ .…

math.GR2023

Virtually free-by-cyclic groups

Dawid Kielak, Marco Linton

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many grou…

math.GR2023

Coherence for elementary amenable groups

Sam Hughes, Dawid Kielak, Peter H. Kropholler +1

We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This genera…

math.GR2022

Quasi-BNS invariants

Nicolaus Heuer, Dawid Kielak

We introduce the notion of quasi-BNS invariants, where we replace homomorphism to $R$ by homogenous quasimorphisms to $R$ in the theory of Bieri-Neumann-Strebel inv…

math.GR2022★ 2 cited

Profinite rigidity of fibring

Sam Hughes, Dawid Kielak

We introduce the classes of TAP groups, in which various types of algebraic fibring are detected by the non-vanishing of twisted Alexander polynomials. We show that finitely presen…

math.GR2022

The Surface Group Conjectures for groups with two generators

Giles Gardam, Dawid Kielak, Alan D. Logan

The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups…

math.GT2021

Agrarian and $ℓ^{2}$ -Betti numbers of locally indicable groups, with a twist

Dawid Kielak, Bin Sun

We prove that twisted $ℓ^{2}$ -Betti numbers of locally indicable groups are equal to the usual $ℓ^{2}$ -Betti numbers rescaled by the dimension of the twisting representation; thi…

math.MG2021

Spectral gap and origami expanders

Goulnara Arzhantseva, Dawid Kielak, Tim de Laat +1

We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus $g > 1$ . We achieve this by finding geometric representatives of multi-twi…

math.GR2021

JSJ decompositions and polytopes for two-generator one-relator groups

Giles Gardam, Dawid Kielak, Alan D. Logan

We provide a direct connection between the Z_{max} (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianis…

math.GR2020

Isoperimetric inequalities for Poincaré duality groups

Dawid Kielak, Peter Kropholler

We show that every oriented $n$ -dimensional Poincaré duality group over a $*$ -ring $R$ is amenable or satisfies a linear homological isoperimetric inequality in dimension $n - 1$ . As…

math.GR2020

$ℓ^{2}$ Betti numbers and coherence of random groups

Dawid Kielak, Robert Kropholler, Gareth Wilkes

We study $ℓ^{2}$ Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coher…

math.AT2019★ 3 cited

The agrarian polytope of two-generator one-relator groups

Fabian Henneke, Dawid Kielak

Relying on the theory of agrarian invariants introduced in previous work, we solve a conjecture of Friedl-Tillmann: we show that the marked polytopes they constructed for two-gener…

math.AT2019

The Farrell-Jones Conjecture for normally poly-free groups

Benjamin Brück, Dawid Kielak, Xiaolei Wu

We prove the $K$ - and $L$ -theoretic Farrell-Jones Conjecture with coefficients in an additive category for every normally poly-free group, in particular for even Artin groups of FC…

math.GT2019★ 1 cited

Handlebody Bundles and Polytopes

Sebastian Hensel, Dawid Kielak

We construct examples of fibered three-manifolds with first Betti number at least 2 and with fibered faces all of whose monodromies extend to a handlebody.

math.GR2019

Non-crossing partitions

Barbara Baumeister, Kai-Uwe Bux, Friedrich Götze +2

Non-crossing partitions have been a staple in combinatorics for quite some time. More recently, they have surfaced (sometimes unexpectedly) in various other contexts from free prob…

math.OA2018★ 5 cited

On property (T) for $Aut (F_{n})$ and $SL_{n} (Z)$

Marek Kaluba, Dawid Kielak, Piotr W. Nowak

We prove that $Aut (F_{n})$ has Kazhdan's property (T) for every $n ⩾ 6$ . Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same state…

math.GR2018★ 38 cited

Residually finite rationally solvable groups and virtual fibring

Dawid Kielak

We show that a finitely generated residually finite rationally solvable (or RFRS) group $G$ is virtually fibred, in the sense that it admits a virtual surjection to $Z$ wi…

Virtual fibring of manifolds and groups

Virtual fibring of Poincaré-duality groups

Non-vanishing unitary cohomology of low-rank integral special linear groups

BNSR invariants and ℓ2-homology

Coboundary expansion and Gromov hyperbolicity

Stallings's Fibring Theorem and PD3-pairs

Kazhdan constants for Chevalley groups over the integers

Group rings of three-manifold groups

Virtually free-by-cyclic groups

Coherence for elementary amenable groups

Quasi-BNS invariants

Profinite rigidity of fibring

The Surface Group Conjectures for groups with two generators

Agrarian and ℓ2-Betti numbers of locally indicable groups, with a twist

Spectral gap and origami expanders

JSJ decompositions and polytopes for two-generator one-relator groups

Isoperimetric inequalities for Poincaré duality groups

ℓ2 Betti numbers and coherence of random groups

The agrarian polytope of two-generator one-relator groups

The Farrell-Jones Conjecture for normally poly-free groups

Handlebody Bundles and Polytopes

Non-crossing partitions

On property (T) for Aut(Fn​) and SLn​(Z)

Residually finite rationally solvable groups and virtual fibring

BNSR invariants and $ℓ^{2}$ -homology

Stallings's Fibring Theorem and $PD^{3}$ -pairs

Agrarian and $ℓ^{2}$ -Betti numbers of locally indicable groups, with a twist

$ℓ^{2}$ Betti numbers and coherence of random groups

On property (T) for $Aut (F_{n})$ and $SL_{n} (Z)$