标题： $C^0$-刚性在辛有理曲面的哈密顿微分同胚群中的表现 显示英文标题

标题： $C^0$-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces

摘要： 我们研究了正辛有理曲面的辛微分同胚群的$C^0$拓扑。 对于少数例外情况以外的所有情况，我们证明了哈密顿微分同胚群在$C^0$拓扑中形成一个连通分支。 这提供了第一个已知哈密顿微分同胚群在辛微分同胚群中为$C^0$闭合的情况。 我们方法的关键是建立对称辛映射类群技术与$C^0$辛拓扑问题之间的桥梁。 通过仔细调整来自$J$全纯叶状结构和膨胀的工具，我们建立了必要的$C^0$距离估计。 我们希望这能作为一个例子，说明这两个子领域如何富有成效地相互作用，并且也提出了由此相互作用产生的几个问题。 显示英文摘要

摘要： We investigate the $C^0$-topology of the group of symplectic diffeomorphisms of positive symplectic rational surfaces. For all but a few exceptions, we prove that the group of Hamiltonian diffeomorphisms forms a connected component in the $C^0$-topology. This provides the first nontrivial case in which the group of Hamiltonian diffeomorphisms is known to be $C^0$-closed inside the group of symplectic diffeomorphisms. The key to our approach is to build a bridge between techniques from symplectic mapping class groups and problems in $C^0$-symplectic topology. Via a careful adaptation of tools from $J$-holomorphic foliation and inflation, we establish the necessary $C^0$-distance estimates. We hope that this serves as an example of how these two subfields can interact fruitfully, and also propose several questions arising from this interplay.