紧辛四维流形只容许有限多个不等价的环面作用
辛几何
2011-04-26 v2
摘要
设 (M,\omega) 为四维紧连通辛流形。我们证明 (M,\omega) 只容许有限多个不等价的哈密顿有效 2-环面作用。因此，若 M 单连通，则辛同胚群 Sympl(M,\omega) 中 2-环面的共轭类个数为有限。我们的证明是“软”的。证明利用了如下事实：对于 \CP^2 的辛吹上，周期映射在例外同调类集合上的限制是恰当的。在附录中，我们描述了 McDuff 的结果，其利用 J-全纯曲线理论给出了一般紧辛四维流形的恰当性结果。
引用
@article{arxiv.math/0609043,
title = {A compact symplectic four-manifold admits only finitely many inequivalent toric actions},
author = {Yael Karshon and Liat Kessler and Martin Pinsonnault},
journal= {arXiv preprint arXiv:math/0609043},
year = {2011}
}
备注
25 pages, 8 figures. Version 2 contains a completely "soft" proof of the main result. The proof in Version 1 used a (soft) lemma about the existence of certain symplectically embedded spheres in toric manifolds. The proof of this lemma has been removed from the published version but it is included in this Eprint as a second appendix