Dawid Kielak

activity

20182022

collaborators

9 papers

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.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.AT2019

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.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

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…