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Abstract 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… Click to show full abstract
Abstract 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}}.
Journal Title: Forum Mathematicum
Year Published: 2017
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