In this paper, we investigate automorphisms of compact Kähler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces $X$ whose groups of $C^\infty$-isotopically trivial automorphisms, resp. cohomologically trivial automorphisms, have a number of connected components which can be arbitrarily large.

中文翻译：

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关于紧 Kähler 流形和代数曲面的拓扑平凡自同构

在本文中，我们研究了具有不同拓扑平凡程度的紧凑 Kähler 流形的自同构。特别地，我们提供了几个光滑复杂射影面 $X$ 的例子，其 $C^\infty$-同位素平凡自同构群分别为。上同调平凡自同构，具有许多可以任意大的连通分量。