Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property |
| |
Authors: | Yi Lin |
| |
Institution: | Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada |
| |
Abstract: | In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples 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. |
| |
Keywords: | Hamiltonian manifold Strong Lefschetz property Symplectic quotient |
本文献已被 ScienceDirect 等数据库收录! |
|