论文标题
汉密尔顿圆圈的中心化行动对理性统治表面
Centralizers of Hamiltonian circle actions on rational ruled surfaces
论文作者
论文摘要
在本文中，我们计算了$ s^2 \ times s^2 $和$ \ mathbb {c} p^2 \＃\ edline {\ mathbb {c} p^2} $在汉密尔顿集团圈子的存在下，$ s^2 \ times s^2 $和$ s^2 \ times s^2 $和$ s^2 $ s^2 $和$ s^2 $ s^2 $和$ s^2 $ s^2 $ s^2 $和$ s^2 $ s^2 $和$ s^2 $和$ \ \ mathbb {c} P^2 \＃我们证明，根据圆圈的作用是至单一的折磨动作还是正好的两个非等量的曲曲曲面作用，具体的符号符号符号符号是同等的，或者是两个圆锥形的同质求职。这是从对兼容和不变的几乎复杂结构$ \ mathcal {j}^{s^1}_Ω$的兼容和不变几乎复杂结构空间的作用的分析。特别是，我们表明此操作保留了$ \ Mathcal {J}^{s^1}_Ω$的分解，并将其与圆圈动作的复曲面扩展进行培养。我们的结果依赖于$ J $ - 摩尔型技术，Delzant对感谢您的动作的分类以及Karshon在$ 4 $ -MANIFOLDS上对Hamiltonian Circle Actions的分类。
In this paper, we compute the homotopy type of the group of equivariant symplectomorphisms of $S^2 \times S^2$ and $\mathbb{C}P^2 \# \overline{\mathbb{C}P^2}$ under the presence of Hamiltonian group actions of the circle $S^1$. We prove that the group of equivariant symplectomorphisms are homotopy equivalent to either a torus, or to the homotopy pushout of two tori depending on whether the circle action extends to a single toric action or to exactly two non-equivalent toric actions. This follows from the analysis of the action of equivariant symplectomorphisms on the space of compatible and invariant almost complex structures $\mathcal{J}^{S^1}_ω$. In particular, we show that this action preserves a decomposition of $\mathcal{J}^{S^1}_ω$ into strata which are in bijection with toric extensions of the circle action. Our results rely on $J$-holomorphic techniques, on Delzant's classification of toric actions and on Karshon's classification of Hamiltonian circle actions on $4$-manifolds.
