collaborators

7 papers

math.GR2025

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.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 admits a virtual epimorphism to the integers whose kernel is itself a Poincaré-duality group over every field if and only if the $L…

math.GT2025

Stallings's Fibring Theorem and -pairs

Martin R. Bridson, Dawid Kielak, Monika Kudlinska

We give a relatively self-contained proof that if a group fibres algebraically and is part of a -pair, then is the fundamental group of a fibred compact asph…

math.GR2024

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 , these ar…

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 of for all of whose invariant vectors are trivial, an…