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# Small Flag Complexes with Torsion

Published:2013-09-30
Printed: Jun 2014
• Michał Adamaszek,
Fachbereich Mathematik, Universität Bremen, Bibliothekstr. 1, 28359 Bremen, Germany
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## Abstract

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
 MSC Classifications: 55U10 - Simplicial sets and complexes 06A11 - Algebraic aspects of posets 55P40 - Suspensions 55-04 - Explicit machine computation and programs (not the theory of computation or programming) 05-04 - Explicit machine computation and programs (not the theory of computation or programming)

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