The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth S1{S^{1}}-action vanishes. In the present work, we prove a version of this result for the integral foliated simplicial volume of aspherical manifolds: The integral foliated simplicial volume of aspherical oriented closed connected smooth manifolds that admit a non-trivial smooth S1{S^{1}}-action vanishes. Our proof uses the geometric construction of Yano’s proof for ordinary simplicial volume as well as the parametrized uniform boundary condition for S1{S^{1}}.

中文翻译：

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整体叶状简单体积和S1作用

允许非平顺S1 {S ^ {1}}作用的定向闭合连接光滑流形的简单体积消失。在当前的工作中，我们证明了非球面流形的整体叶单纯形体积的这一结果的一个版本：非球面定向封闭连通光滑流形的整体叶形单纯体积允许非平凡光滑S1 {S ^ {1}}-行动消失了。我们的证明使用Yano证明的几何构造（用于普通的简单体积）以及S1 {S ^ {1}}的参数化统一边界条件。