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Small Flag Complexes with Torsion

Published online by Cambridge University Press:  20 November 2018

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

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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

55U1006A1155P4055-0405-04clique complexorder complexhomologytorsionminimal model

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 225 - 230
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

This research was carried out when the author was a member of the Centre for Discrete Mathematics and its Applications (DIMAP) and the Mathematics Institute of the University of Warwick, Coventry, UK. The support of EPSRC award EP/D063191/1 is gratefully acknowledged.

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