Odd manifolds of small integral simplicial volume

Clara Löh Universität Regensburg

Geometric Analysis and Geometric Topology mathscidoc:1912.43021

Arkiv for Matematik, 56, (2), 351 – 375, 2018
Integral simplicial volume is a homotopy invariant of oriented closed connected manifolds, defined as the minimal weighted number of singular simplices needed to represent the fundamental class with integral coefficients. We show that odd-dimensional spheres are the only manifolds with integral simplicial volume equal to 1. Consequently, we obtain an elementary proof that, in general, the integral simplicial volume of (triangulated) manifolds is not computable.
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  title={Odd manifolds of small integral simplicial volume},
  author={Clara Löh},
  booktitle={Arkiv for Matematik},
  pages={351 – 375},
Clara Löh. Odd manifolds of small integral simplicial volume. 2018. Vol. 56. In Arkiv for Matematik. pp.351 – 375. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204103755082543577.
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