We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely the ones that arise through a ramified covering. These are the main known examples of bundles with non-zero signature.

中文翻译：

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曲面上的曲面丛：签名、单纯体积和欧拉特征之间的新不等式

我们提出了三个新的不等式，这些不等式将表面丛的签名、单纯体积和表面丛的欧拉特征联系起来。其中两个适用于任何表面丛，而第三个适用于特定的表面丛家族，即通过分枝覆盖产生的表面丛。这些是具有非零签名的包的主要已知示例。