Integral foliated simplicial volume and S 1-actions

Author:

Fauser Daniel1ORCID

Affiliation:

1. Fakultät für Mathematik , Universität Regensburg , 93040 Regensburg , Germany

Abstract

Abstract The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth S 1 {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 {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 S 1 {S^{1}} .

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference22 articles.

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4. D. Fauser, Parametrised simplicial volume and S1S^{1}-actions, PhD thesis, Universität Regensburg, 2019, https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-404319.

5. D. Fauser, S. Friedl and C. Löh, Integral approximation of simplicial volume of graph manifolds, Bull. Lond. Math. Soc. 51 (2019), no. 4, 715–731.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the simplicial volume and the Euler characteristic of (aspherical) manifolds;Research in the Mathematical Sciences;2022-07-14

2. Volume and macroscopic scalar curvature;Geometric and Functional Analysis;2021-12-28

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