Integral foliated simplicial volume and $S^1$-actions

Daniel Fauser

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arXiv · 1704.08538

Integral foliated simplicial volume and $S^1$-actions

Daniel Fauser

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Abstract

The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth $S^1$-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 $S^1$-action vanishes. Our proof uses the geometric construction of Yano's proof for ordinary simplicial volume as well as the parametrised uniform boundary condition for $S^1$.

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Daniel Fauser. 2017-04-27. Integral foliated simplicial volume and $S^1$-actions. https://arxiv.org/abs/1704.08538

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