可积Kähler群
Cubulable Kähler groups
摘要：
我们证明了一个可积的Kähler群，即它在CAT（0）三次复形上适当地不连续和余紧，有一个同构于曲面群的一个直积的有限指数子群，可能有一个自由的阿贝尔因子.类似地，我们证明了具有可积基本群的闭非球面Kähler流形有一个有限覆盖，该覆盖双全纯于黎曼曲面乘积上的拓扑平凡主环面丛。在此过程中，我们证明了Kähler群在不可约的局部有限CAT（0）三次复形上的基本作用的因式分解结果，假设在视觉边界上没有不动点。
英文摘要：
We prove that a Kähler group which is cubulable, i.e. which acts properly discontinuously and cocompactly on a CAT(0) cubical complex, has a finite index subgroup isomorphic to a direct product of surface groups, possibly with a free Abelian factor. Similarly, we prove that a closed aspherical Kähler manifold with a cubulable fundamental group has a finite cover which is biholomorphic to a topologically trivial principal torus bundle over a product of Riemann surfaces. Along the way, we prove a factorization result for essential actions of Kähler groups on irreducible, locally finite CAT(0) cubical complexes, under the assumption that there is no fixed point in the visual boundary.
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