Geodesic
Small Flag Complexes with Torsion
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 225-230

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DOI

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.
DOI : 10.4153/CMB-2013-032-9
Mots-clés : 55U10, 06A11, 55P40, 55-04, 05-04, clique complex, order complex, homology, torsion, minimal model 
Adamaszek, Michał. Small Flag Complexes with Torsion. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 225-230. doi: 10.4153/CMB-2013-032-9
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     author = {Adamaszek, Micha{\l}},
     title = {Small {Flag} {Complexes} with {Torsion}},
     journal = {Canadian mathematical bulletin},
     pages = {225--230},
     year = {2014},
     volume = {57},
     number = {2},
     doi = {10.4153/CMB-2013-032-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-032-9/}
}
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