Canad. Math. Bull. 57(2014), 225-230
Printed: Jun 2014
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.
clique complex, order complex, homology, torsion, minimal model
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)