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Five-torsion in the homology of the matching complex on 14 vertices
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2009 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 29, no 1, 81-90 p.Article in journal (Refereed) Published
Abstract [en]

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 M-14 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 M-n when n = 13 and n not equal 14.

Place, publisher, year, edition, pages
2009. Vol. 29, no 1, 81-90 p.
Keyword [en]
Matching complex, Simplicial homology, Torsion subgroup, degree graph complexes, chessboard complexes
URN: urn:nbn:se:kth:diva-18070DOI: 10.1007/s10801-008-0123-6ISI: 000261988800004ScopusID: 2-s2.0-58149147075OAI: diva2:336116
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-10Bibliographically approved

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