关于辛映射拟态射的连续性
On continuity of quasi-morphisms for symplectic maps
摘要：
讨论了辛流形的紧支撑辛同构群的单位连通区上的$C^0$ -连续齐次拟态射.这样的拟态射扩展到同胚群内的这个群的$C^0$ -闭包。我们表明，对于标准的辛球的任何维度，以及紧凑的定向表面，其他的领域，这样的准态射的空间是无限维的。在曲面的情况下，我们给出了一个用户友好的拓扑特征，这样的准态射。我们还提出了一个应用程序，以哈立德的几何群的哈密顿同胚的球。
英文摘要：
We discuss $C^0$-continuous homogeneous quasi-morphisms on the identity component of the group of compactly supported symplectomorphisms of a symplectic manifold. Such quasi-morphisms extend to the $C^0$-closure of this group inside the homeomorphism group. We show that for standard symplectic balls of any dimension, as well as for compact oriented surfaces, other than the sphere, the space of such quasi-morphisms is infinite-dimensional. In the case of surfaces, we give a user-friendly topological characterization of such quasi-morphisms. We also present an application to Hofer's geometry on the group of Hamiltonian diffeomorphisms of the ball.
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