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1
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On compact symplectic and Kählerian solvmanifolds which are not completely solvable

100%
Tralle A.
Colloquium Mathematicum
|
1997
|
tom 73
|
nr 2
261-283
EN
We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.
2
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Fat bundles and formality

64%
Andrzejewski W., Tralle A.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 2
105-118
EN
We prove the formality property of total spaces of fat bundles over compact homogeneous spaces. Some rational homotopy obstructions to fatness are obtained.
3
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A Note on Hamiltonian Lie Group Actions and Massey Products

64%
Stępień Z., Tralle A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
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tom 52
|
nr 2
141-149
EN
We show that the property of having only vanishing triple Massey products in equivariant cohomology is inherited by the set of fixed points of hamiltonian circle actions on closed symplectic manifolds. This result can be considered in a more general context of characterizing homotopic properties of Lie group actions. In particular it can be viewed as a partial answer to a question posed by Allday and Puppe about finding conditions ensuring the "formality" of G-actions.
4
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Generalized symmetric spaces and minimal models

51%
Dumańska-Małyszko A., Stępień Z., Tralle A.
Annales Polonici Mathematici
|
1996
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tom 64
|
nr 1
17-35
EN
We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.
5
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On curvature constructions of symplectic forms

51%
Szczepkowska A., Tralle A., Woike A.
Banach Center Publications
|
2011
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tom 93
|
nr 1
261-269
EN
We generalize the result of Lerman [Letters Math. Phys. 15 (1988)] concerning the condition of fatness of the canonical connection in a certain principal fibre bundle. We also describe new classes of symplectically fat bundles: twistor budles over spheres, bundles over quaternionic Kähler homogeneous spaces and locally homogeneous complex manifolds.
6
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Introduction

20%
Oprea J., Tralle A.
Banach Center Publications
|
1998
|
tom 45
|
nr 1
7-11
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