论文标题
均质的准态，$ C^0 $ - 学术和拉格朗日交叉点
Homogeneous quasimorphisms, $C^0$-topology and Lagrangian intersection
论文作者
论文摘要
我们构建了一个非平凡的均匀二态性的示例，上面是两个和四个维度四维超曲面的哈密顿型差异性，相对于$ c^0 $ metric和hofer metric，这是连续的。这回答了Entov- polterovich-Py问题的一种变体，这是McDuff-Salamon专着中列出的开放问题之一。在整个证明过程中，我们广泛利用与量子同胞环中不同系数领域合作的想法。作为本文中论点的副产品，我们回答了一个关于复杂射击平面的汉密尔顿二型差异性的准晶体的问题 - wu，并证明了四个二维四维四维高度超曲面的拉格朗日的一些交叉点。
We construct an example of a non-trivial homogeneous quasimorphism on the group of Hamiltonian diffeomorphisms of the two and four dimensional quadric hypersurfaces which is continuous with respect to both the $C^0$-metric and the Hofer metric. This answers a variant of a question of Entov--Polterovich--Py which is one of the open problems listed in the monograph of McDuff--Salamon. Throughout the proof, we make extensive use of the idea of working with different coefficient fields in quantum cohomology rings. As a by-product of the arguments in the paper, we answer a question of Polterovich--Wu regarding quasimorphisms on the group of Hamiltonian diffeomorphisms of the complex projective plane and prove some intersection results about Lagrangians in the four dimensional quadric hypersurface.
