Arkiv för Matematik

Volume 56 (2018)

Number 2

Odd manifolds of small integral simplicial volume

Pages: 351 – 375

DOI: http://dx.doi.org/10.4310/ARKIV.2018.v56.n2.a10

Author

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

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.

2010 Mathematics Subject Classification

55N10, 57N65

Full Text (PDF format)

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