Examples of Non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

Details Examples of Non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property Examples of Non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

2004-08-25

arxiv.org/abs/math/0408345v3

Mathematics

Symplectic Geometry

This is the final version which is going to appear in Advances in Math. The proof of the main result gets simplified

Scientific paper

In this paper we construct six-dimensional compact non-K\"ahler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counter examples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.

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