1. CMB 2013 (vol 57 pp. 225)
||Small Flag Complexes with Torsion|
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.
Keywords:clique complex, order complex, homology, torsion, minimal model
Categories:55U10, 06A11, 55P40, 55-04, 05-04