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Small Flag Complexes with Torsion

Published online by Cambridge University Press:  20 November 2018

Michał Adamaszek
Affiliation:
Fachbereich Mathematik, Universität Bremen, Bibliothekstr. 1, 28359 Bremen, Germany e-mail: aszek@mimuw.edu.pl
Corresponding
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2014

References

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