FIVE-TORSION IN THE HOMOLOGY OF THE MATCHING COMPLEX ON 14 VERTICES
Jakob Jönsson · 2015
Abstract. J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex M14 on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case n = 14 is exceptional; for all other n, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of Mn when n ≥ 13 and n 6 = 14. This is a preprint version of a paper to appear in the Journal of Algebraic Combi-natorics. The original publication will be available at www.springerlink.com. 1.