147 citations · 257 across the 20 of their papers we have counts for
21 papers
A refinement of bounded cohomology
Światosław R. Gal, Jarek Kędra
We introduce a refinement of bounded cohomology and prove that the suitable comparison homomorphisms vanish for an amenable group. We investigate in this context Thompson's group F…
Reflection length with two parameters in the asymptotic representation theory of type B/C and applications
Marek Bożejko, Maciej Dołęga, Wiktor Ejsmont +1
We introduce a two-parameter function on the infinite hyperoctahedral group, which is a bivariate refinement of the reflection length keeping track of the long and th…
Finite index subgroups in Chevalley groups are bounded: an addendum to "On bi-invariant word metrics"
Światosław R. Gal, Jarek Kędra, Alexander A. Trost
We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.
Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability
Marek Bożejko, Światosław R. Gal, Wojciech Młotkowski
A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-C…
Uniform symplicity of groups with proximal action
Światosław R. Gal, Jakub Gismatullin, Nir Lazarovich
We prove that groups acting boundedly and order-primitively on linear orders or acting extremly proximality on a Cantor set (the class including various Higman-Thomson groups and N…
On approximation properties of semidirect products of groups
Goulnara Arzhantseva, Światosław R. Gal
Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residuall…
Cancelation norm and the geometry of biinvariant word metrics
Michael Brandenbursky, Światosław R. Gal, Jarek Kędra +1
We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isomet…
Curvature spectra of simple Lie groups
Andrzej Derdzinski, Swiatoslaw R. Gal
The Killing form β of a real (or complex) semisimple Lie group G is a left-invariant pseudo-Riemannian (or, respectively, holomorphic) Einstein metric. Let Ω denote the multiple of…
On distortion in groups of homeomorphisms
Światosław Gal, Jarek Kędra
Let X be a path-connected topological space admitting a universal cover. Let Homeo(X,a) denote the group of homeomorphisms of X preserving degree one cohomology class a. We investi…
\int_x^{hx}(g^*α-α)
Światosław R. Gal, Jarek Kędra
Let X be a connected topological space admitting a universal cover. Let a be a degree one cohomology class on X. We define and study a two-cocycle on a group acting on X by homeomo…
A two-cocycle on the group of symplectic diffeomorphisms
Światosław R. Gal, Jarek Kędra
We investigate a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifolds defined by Ismagilov, Losik, and Michor and investigate its properties. We…
On the algebraic independence of Hamiltonian characteristic classes
Swiatoslaw Gal, Jarek Kedra, Aleksy Tralle
We prove that Hamiltonian characteristic classes defined as fibre integrals of powers of the coupling class are algebraically independent for generic coadjoint orbits.
Odd-dimensional Charney-Davis conjecture
Swiat R. Gal, Tadeusz Januszkiewicz
More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dim…
A cocycle on the group of symplectic diffeomorphisms
Swiatoslaw R. Gal, Jarek Kedra
We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions…
Asymptotic dimension and uniform embeddings
S. R. Gal
We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any ) compression. The method allows to obtain the lower bound of the comp…
Symplectic configurations
Swiat Gal, Jarek Kedra
We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties a…
On Normal Subgroups of Coxeter Groups Generated by Standard Parabolic Subgroups
Swiatoslaw R. Gal
We discuss one construction of nonstandard subgroups in the category of Coxeter groups. Two formulae for the growth series of such a subgroups are given. As an application we const…
Real Root Conjecture fails for five and higher dimensional spheres
Swiatoslaw R. Gal
A construction of convex flag triangulations of five and higher dimensional spheres, whose h-polynomials fail to have only real roots, is given. We show that there is no such examp…
a-T-menability of groups acting on trees
Swiatoslaw R. Gal
We present some partial results concerning a-T-menability of groups acting on trees. Various known results are given uniform proofs.
Euler characteristic of the configuration space of a complex
S. R. Gal
A closed form formula (generating function) for the Euler characteristic of the configuration space of particles in a simplicial complex is given.
a-T-menability of Baumslag-Solitar groups
S. R. Gal, T. Januszkiewicz
The Baumslag-Solitar groups and their certain variations are a-T-menable. This is proved by embeding them into topological groups and studying representation theoretic properties o…