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A Note on Hamiltonian Lie Group Actions and Massey Products

100%

Stępień Z., Tralle A.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

tom 52

nr 2

141-149

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.

Generalized symmetric spaces and minimal models

81%

Dumańska-Małyszko A., Stępień Z., Tralle A.

Annales Polonici Mathematici

1996

tom 64

nr 1

17-35

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Bulletin of the Polish Academy of Sciences. Mathematics

2 Stępień Z.

2 Tralle A.

1 Dumańska-Małyszko A.

1 2004

1 1996

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A Note on Hamiltonian Lie Group Actions and Massey Products

Generalized symmetric spaces and minimal models