Abstract
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.
Funding Statement
This work was supported by the CRC 1085 Higher Invariants (Universität Regensburg, funded by the DFG).
Citation
Clara Löh. "Odd manifolds of small integral simplicial volume." Ark. Mat. 56 (2) 351 - 375, October 2018. https://doi.org/10.4310/ARKIV.2018.v56.n2.a10