38 citations · 139 across the 31 of their papers we have counts for
23 papers · 1 filter
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…
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^2…
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, and…
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…
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…
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…
Quasi-BNS invariants
Nicolaus Heuer, Dawid Kielak
We introduce the notion of quasi-BNS invariants, where we replace homomorphism to by homogenous quasimorphisms to in the theory of Bieri-Neumann-Strebel inv…
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…
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…
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…
Isoperimetric inequalities for Poincaré duality groups
Dawid Kielak, Peter Kropholler
We show that every oriented -dimensional Poincaré duality group over a -ring is amenable or satisfies a linear homological isoperimetric inequality in dimension . As…
Betti numbers and coherence of random groups
Dawid Kielak, Robert Kropholler, Gareth Wilkes
We study Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coher…
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…
Residually finite rationally solvable groups and virtual fibring
Dawid Kielak
We show that a finitely generated residually finite rationally solvable (or RFRS) group is virtually fibred, in the sense that it admits a virtual surjection to wi…
The Bieri-Neumann-Strebel invariants via Newton polytopes
Dawid Kielak
We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather…
On the smallest non-trivial quotients of mapping class groups
Dawid Kielak, Emilio Pierro
We prove that the smallest non-trivial quotient of the mapping class group of a connected orientable surface of genus at least 3 without punctures is , thus co…
On the smallest non-abelian quotient of
Barbara Baumeister, Dawid Kielak, Emilio Pierro
We show that the smallest non-abelian quotient of is , thus confirming a conjecture of Mecchia--Zimmer…
Outer actions of on small right-angled Artin groups
Dawid Kielak
We determine the precise conditions under which , the unique index two subgroup of , can act non-trivially via outer automorphisms on a RAAG…
Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groups
Florian Funke, Dawid Kielak
We investigate Friedl-Lück's universal -torsion for descending HNN extensions of finitely generated free groups, and so in particular for -by- groups. This in…
Nielsen Realisation by Gluing: Limit Groups and Free Products
Sebastian Hensel, Dawid Kielak
We generalise the Karrass-Pietrowski-Solitar and the Nielsen realisation theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point the…
The 6-strand braid group is CAT(0)
Thomas Haettel, Dawid Kielak, Petra Schwer
We show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes and the embeddability o…
Low dimensional free and linear representations of
Dawid Kielak
We study homomorphisms from to , and for , where is a field of characteristic other than 2 or 3. We conclude th…
Outer automorphism groups of free groups: linear and free representations
Dawid Kielak
We study the existence of homomorphisms between Out(F_n) and Out(F_m) for n > 5 and m < n(n-1)/2, and conclude that if m is not equal to n then each such homomorphism factors throu…