哈密尔顿伪表示
Hamiltonian pseudo-representations
摘要：
这里研究的问题是泊松括号在C^0-扰动下的行为。为此，我们引入了伪表示的概念，并证明了赋范李代数收敛于一个表示。这个结果的一个意想不到的结果是，对于许多非闭的辛流形（包括余切丛），Hamilton复同态群（没有关于支撑的假设）没有C^{-1}双不变度量。我们的方法还提供了Gromov-Eliashberg定理的一个新的证明，即辛同态群在所有辛同态群中是C^0-闭的。
英文摘要：
The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An unexpected consequence of this result is that for many non-closed symplectic manifolds (including cotangent bundles), the group of Hamiltonian diffeomorphisms (with no assumptions on supports) has no C^{-1} bi-invariant metric. Our methods also provide a new proof of Gromov-Eliashberg Theorem, it is to say that the group of symplectic diffeomorphisms is C^0-closed in the group of all diffeomorphisms.
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