Small Flag Complexes with Torsion

Canadian mathematical bulletin

Michał Adamaszek¹ 

[1] Fachbereich Mathematik, Universität Bremen, Bibliothekstr. 1, 28359 Bremen, Germany

关键词: clique complex;    order complex;    homology;    torsion;    minimal model;   

DOI  :  10.4153/CMB-2013-032-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We classify flag complexes on at most $12$ vertices with torsion inthe first homology group. The result is moderately computer-aided. As a consequence we confirm a folklore conjecture that the smallestposet whose order complex is homotopy equivalent to the realprojective plane (and also the smallest poset with torsion in thefirst homology group) has exactly $13$ elements.

【 授权许可】

Unknown