9 citations · 30 across the 16 of their papers we have counts for
21 papers
Exotic proper actions on homogeneous spaces via convex cocompact representations
Maciej Bochenski, Yosuke Morita
We construct a series of homogeneous spaces G/H of reductive type which admit proper actions of discrete subgroups of G isomorphic to cocompact lattices of O(n,1) (n=2,3,4) but do…
A solution of the problem of standard compact Clifford-Klein forms
Maciej Bochenski, Aleksy Tralle
We solve the long standing problem of classification of standard compact Clifford-Klein forms of homogeneous spaces of simple non-compact real Lie groups under the extra assumption…
Standard compact Clifford-Klein forms and Lie algebra decompositions
Maciej Bochenski, Aleksy Tralle
We find relations between real root decompositions of triples of Lie algebras corresponding to standard compact Clifford-Klein forms, under the assumption that these triples are no…
Stretched non-positive Weyl connections on solvable Lie groups
Maciej Bochenski, Piotr Jastrzebski, Aleksy Tralle
We determine the structure of solvable Lie groups endowed with invariant stretched non-positive Weyl connections and find classes of solvable Lie groups admitting and not admitting…
Non-virtually abelian discontinuous group actions vs. proper SL(2,R)-actions on homogeneous spaces
Maciej Bochenski, Willem A. de Graaf, Piotr Jastrzebski +1
We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new ex…
Homogeneous spaces of real simple Lie groups with proper actions of non virtually abelian discrete subgroups: a calculational approach
Maciej Bochenski, Piotr Jastrzebski, Aleksy Tralle
Let G be a simple non-compact linear connected Lie group and H be a closed non-compact semisimple subgroup. We are interested in finding classes of homogeneous spaces G/H admitting…
On semisimple standard compact Clifford-Klein forms
Maciej Bocheński
In this paper we give the classification of standard compact Clifford-Klein forms corresponding to triples (g,h,l) such that g = h+l and g is a sum of two absolutely simple ideals.…
On locally homogeneous pseudo-Riemannian compact einstein manifolds
Maciej Bochenski, Aleksy Tralle
We ask a general question: what are locally homogeneous compact pseudo-Riemannian Einstein manifolds? We show that any standard compact Clifford-Klein form of a simple non-compact…
Non-existence of standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups
Maciej Bochenski, Piotr Jastrzebski, Aleksy Tralle
We use a computer-aided approach to prove that there are no standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups. This yields further support for K…
Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford-Klein forms problem
Maciej Bocheński, Piotr Jastrzębski, Anna Szczepkowska +2
In this paper we develop algorithms of finding homogeneous spaces of semisimple non-compact Lie groups which do not admit compact Clifford-Klein forms. We propose a computer progra…
Totally non cohomologous to zero fibrations and amenable Clifford-Klein forms of 3-symmetric spaces
Maciej Bochenski, Aleksy Tralle
We prove that 3-symmetric spaces of simple linear real Lie groups do not admit amenable compact Clifford-Klein forms. Our basic tool are totally non cohomologous to zero fibrations…
On the Hirzebruch-Kobayashi-Ono proportionality principle and the non-existence of compact solvable Clifford-Klein forms of certain homogeneous spaces
Maciej Bochenski, Aleksy Tralle
This article continues a line of research aimed at solving an important problem of T. Kobayashi of the existence of compact Clifford-Klein forms of reductive homogeneous spaces. We…
On a classification of fat bundles over compact homogeneous spaces
Maciej Bochenski, Anna Szczepkowska, Aleksy Tralle +1
This article deals with fat bundles. Berard-Bergery classified all homogeneous bundles of that type. We ask a question of a possibility to generalize his description in the case of…
On solvable compact Clifford-Klein forms
Maciej Bochenski, Aleksy Tralle
In this article we prove that under certain assumptions, a reductive homogeneous space G/H does not admit a solvable compact Clifford-Klein form. This generalizes the well known no…
New constructions of symplectically fat fiber bundles
Maciej Bochenski, Anna Szczepkowska, Aleksy Tralle +1
This work is devoted to new constructions of symplectically fat fiber bundles. The latter are constructed in two ways: using the Kirwan map and expressing the fatness condition in…
Proper actions on strongly regular homogeneous spaces
Maciej Bochenski
Let G/H be a strongly regular homogeneous space such that H is a Lie group of inner type. We show that G/H admits a proper action of a discrete non-virtually abelian subgroup of G…
On symplectically fat twistor bundles
Maciej Bochenski, Anna Szczepkowska, Aleksy Tralle +1
This paper deals with the question when are twistor bundles over homogeneous spaces symplectically fat? It shows that twistor bundles over even dimensional Grassmannians of maximal…
A restriction on proper actions on homogeneous spaces of reductive type
Maciej Bochenski, Marek Ogryzek
Let L be a reductive subgroup of a reductive Lie group G. Let G/H be a homogeneous space of reductive type. We provide a necessary condition for the properness of the action of L o…
Proper SL(2,R)-actions on homogeneous spaces
Maciej Bochenski, Piotr Jastrzebski, Takayuki Okuda +1
We study the existence problem of proper actions of SL(2,R) on homogeneous spaces G/H of reductive type. Based on Kobayashi's properness criterion [Math. Ann. (1989)], we show that…
Clifford-Klein forms and a-hyperbolic rank
Maciej Bochenski, Aleksy Tralle
The porpose of this article is to introduce and investigate properties of a tool (the a-hyperbolic rank) which enables us to obtain new examples of homogeneous spaces G/H which adm…
Generalized symplectic symmetric spaces
Maciej Bochenski, Aleksy Tralle
Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since…