Arkiv för Matematik

Volume 56 (2018)

Number 2

Odd manifolds of small integral simplicial volume

Pages: 351 – 375



Clara Löh (Fakultät für Mathematik, Universität Regensburg, Germany)


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.

2010 Mathematics Subject Classification

55N10, 57N65

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This work was supported by the CRC 1085 Higher Invariants (Universität Regensburg, funded by the DFG).

Received 15 March 2017

Received revised 31 July 2017