Published online by Cambridge University Press: 20 November 2018
We classify flag complexes on at most 12 vertices with torsion in the first homology group. The result is moderately computer-aided.
As a consequence we confirm a folklore conjecture that the smallest poset whose order complex is homotopy equivalent to the real projective plane (and also the smallest poset with torsion in the first homology group) has exactly 13 elements.
This research was carried out when the author was a member of the Centre for Discrete Mathematics and its Applications (DIMAP) and the Mathematics Institute of the University of Warwick, Coventry, UK. The support of EPSRC award EP/D063191/1 is gratefully acknowledged.