5 citations · 6 across the 7 of their papers we have counts for
9 papers
On vanishing and Hausdorffness of asymptotic cohomology
Alexis Marchand, Piotr W. Nowak
Asymptotic cohomology was recently introduced to study stability problems in group theory. This paper studies vanishing and Hausdorffness questions around asymptotic cohomology. Ou…
Property and nonlinearity of mapping class group quotients
Piotr W. Nowak
We give a general method for proving Kazhdan's property for quotients , where is countable, is a normal subgroup and denotes its lower central…
Cocycles and positive functionals in higher cohomology
Antonio López Neumann, Piotr W. Nowak
We establish and explore the correspondence between positive functionals and cocycles in higher unitary cohomology. We generalize the classical cocycle version of the Gelfand-Naima…
Coboundary expansion and Gromov hyperbolicity
Dawid Kielak, Piotr W. Nowak
We prove that if a compact -manifold admits a sequence of residual covers that form a coboundary expander in dimension , then the manifold has Gromov-hyperbolic fundamental…
On (bi)reversible automata generating lamplighter groups
Piotr W. Nowak, Andriy Oliynyk, Veronika Prokhorchuk
For any nontrivial abelian group we construct a reversible (bireversible in case the order of is odd) automaton such that its set of states and alphabet a…
On order units in the augmentation ideal
Piotr Mizerka, Piotr W. Nowak
We study order units in the real group ring and the augmentation ideal, as well as in matrix algebras. We identify an infinite family of order units in the powers of the augmentati…
Spectral gap for the cohomological Laplacian of
Marek Kaluba, Piotr Mizerka, Piotr W. Nowak
We show that the cohomological Laplacian in degree 1 in the group cohomology of is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb…
Group 1-cohomology is complemented
Piotr W. Nowak
We show a structural property of cohomology with coefficients in an isometric representation on a uniformly convex Banach space: if the cohomology group is reduced, then…
Controlled coarse homology and isoperimetric inequalities
Piotr Nowak, Jan Spakula
We study a coarse homology theory with prescribed growth conditions. For a finitely generated group G with the word length metric this homology theory turns out to be related to am…