In this paper, we prove homological stability of symplectomorphisms and extended hamiltonians of surfaces made discrete. We construct an isomorphism from the stable homology group of symplectomorphisms and extended Hamiltonians of surfaces to the homology of certain infinite loop spaces. We use these infinite loop spaces to study characteristic classes of surface bundles whose holonomy groups are area preserving, in particular we give a homotopy theoretic proof of the Kotschick-Morita theorem.

中文翻译：

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关于平辛面丛的模空间

在本文中，我们证明了离散表面的辛同胚和扩展哈密顿量的同调稳定性。我们从辛同胚的稳定同调群和曲面的扩展哈密顿量构造一个同构到某些无限循环空间的同构。我们使用这些无限循环空间来研究表面丛的特征类，其完整群是区域保持的，特别是我们给出了 Kotschick-Morita 定理的同伦理论证明。