Integral foliated simplicial volume and $S^1$-actions
Geometric Topology
2019-08-20 v4
Abstract
The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth -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 -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 .
Cite
@article{arxiv.1704.08538,
title = {Integral foliated simplicial volume and $S^1$-actions},
author = {Daniel Fauser},
journal= {arXiv preprint arXiv:1704.08538},
year = {2019}
}
Comments
18 pages; v2: typo in abstract, improved introduction, added missing notation; v3: added applications, generalisation to compact manifolds possibly with boundary; v4: updated the introduction and references