L^ \infty -范数下的Hamilton同胚群
The Group of Hamiltonian Homeomorphisms in the L^\infty-norm
摘要：
在[7]和[6]中定义并研究了连通辛流形（M，ω）的Hamilton同胚群Hameo（M，ω）.在这些论文中，作者在哈密尔顿路径空间上一致地使用L^{（1，\infty）}-Hynth范数（而不是L^ \infty -Hynth范数）（定义见下文）。在[7]中给出了这种选择的理由。本文研究L^ \infty -情形。考虑到Hamilton同构群Ham（M，ω）上的Ham范数不依赖于L^{（1，\infty）}-范数与L^ \infty -范数的选择[9]，Y. G.哦，D。McDuff（私人通信）问是否两个概念的哈密顿同胚产生的不同的规范一致。本文将对这一问题给予肯定的回答。
英文摘要：
The group Hameo (M,ω) of Hamiltonian homeomorphisms of a connected symplectic manifold (M,ω) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the L^{(1,\infty)}-Hofer norm (and not the L^\infty-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the L^\infty-case. In view of the fact that the Hofer norm on the group Ham (M,ω) of Hamiltonian diffeomorphisms does not depend on the choice of the L^{(1,\infty)}-norm vs. the L^\infty-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.
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