Światosław R. Gal

  Instytut Matematyczny UWr           /"\
  pl. Grunwaldzki 2/4                 \ /     ASCII RIBBON CAMPAIGN
  50-384 Wrocław, POLOGNE              X        AGAINST HTML MAIL
  Swiatoslaw.Gal at math.uni.wroc.pl  / \/

Research Papers:

Reviews on MathSciNet, BibTeX

Odd-dimensional Charney-Davis Conjecture (dvi, pdf)

with Tadeusz Januszkiewicz
in Discrete & Computational Geometry, on-line
arXiv: 0905.1961

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-dimensional spheres.

A cocycle on the group of symplectic diffeomorphisms (dvi, pdf)

with Jarek Kedra
accepted by Advances in Geometry
arXiv: 0807.1191

We define a cocycle on the group of symplectic diffeomorphisms of a symplecticaly aspherical manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative proof of the Polterovich theorem about the distortion of cyclic subgroups in finitely generated groups of Hamiltonian diffeomorphisms.

Asymptotic dimension and uniform embeddings (dvi, pdf)

in Groups, Geometry, and Dynamics, Volume 2, Issue 1, 2008, pp. 63–84
arXiv: math.GT/0607376

We study uniform embeddings of metric spaces satisfying some asymptotic tameness conditions such as finite asymptotic dimension, finite Assouad-Nagata dimension, polynomial dimension growth or polynomial growth into function spaces.
We show how the type function of a space with finite asymptotic dimension estimates its Hilbert (or any l^p-) compression. In particular, we show that the spaces of finite asymptotic dimension with linear type (spaces with finite Assouad-Nagata dimension) have compression rate equal to one.
We show, without an extra assumption that the space has doubling property (finite Assouad dimension), that a space with polynomial growth has polynomial dimension growth and compression rate equal to one.
The method allows to obtain the lower bound of the compression of the lamplighter group Z≀Z, which has infinite asymptotic dimension.

Symplectic Configurations (dvi, pdf)

with Jarek Kedra
in International Mathematics Research Notices, Volume 2006 (2006)
arXiv: math.SG/0504100

We define a class of symplectic fibrations called symplectic configurations. They are a natural generalization of Hamiltonian fibrations in the sense that they admit closed symplectic connection two-form. Their geometric and topological properties are investigated. We are mainly concentrated on integral symplectic manifolds.
We construct the classifying space Б of symplectic integral configurations. The properties of the classifying map Б→BSymp(M,ω) are examined. The universal symplectic bundle over Б has a natural connection whose holonomy group is the enlarged Hamiltonian group recently defined by McDuff. The space Б is identified with the classifying space of an extension of certain subgroup of the symplectomorphism group.

Real Root Conjecture fails for five and higher dimensional spheres (dvi, pdf)

in Discrete & Computational Geometry, Vol. 34 (2005) Number 2, pp. 269-284
arXiv: math.CO/0501046

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 example in dimensions lower than five.
A conditon weaker than realrootedness is conjectured and some evidence is provided.

Normal subgroups of Coxeter groups (dvi, pdf)

in Geometriae Dedicata Vol. 115 (2005), pp. 65-78
arXiv: math.GR/0502563

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 construct a flag simple convex polytope, whose f-polynomial has non-real roots.

a-T-menability of groups acting on trees (dvi, pdf)

in the Bulletin of the Australian Mathematical Society, Vol. 69 (2004) pp. 297--303
arXiv: math.GR/0311217

We present some partial results concerning a-T-menability of groups acting on trees. Various known results are given uniform proofs.

New a-T-menable HNN extensions (dvi, pdf)

with Tadeusz Januszkiewicz
in Journal of Lie Theory, Vol. 13 (2003), No. 2, pp. 383--385
arXiv: math.GR/0202047 (older version, without some minor changes; under old title)

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 of the latter.
The paper is motivated by the questions of A. Valette.

Euler characteristic of a configuration space of a complex (dvi, pdf),

in Colloquium Mathematicum Volume 89 (2001), Issue 1, pp. 61--67
arXiv: math.GN/0202143

A closed form formula (generating function) for the Euler characteristic of the configuration space of n particles in a simplicial complex is given.

Posters, Transpanrencies etc. (stuff not expected to be published):

(04.'05) Counting faces of flag spheres (pdf),

(06.'04) On the Poles of the Growth Series of Coxeter Groups (dvi, pdf),

We present an overview of the problems connected with the number of real roots of the growth serie of Coxeter groups.

(02.'03) Concentration Conjecture and Morse Inequalities (dvi)

(11.'00) Uniform distribution of the Fibbonacci sequence (dvi)

Papers in formal languages:

gsteinberg (tar.gz)

Simple C program that finds all finite type subgraphs of a given Dynkin diagram plus gtk-1.2 GUI. Free.