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Exact sequences for the homology of the matching complex
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 115, no 8, p. 1504-1526Article in journal (Refereed) Published
Abstract [en]

Building on work by Bouc and by Shareshian and Wachs, we provide a toolbox of long exact sequences for the reduced simplicial homology of the matching complex M., which is the simplicial complex of matchings in the complete graph K-n. Combining these sequences in different ways, we prove several results about the 3-torsion part of the homology of M, First, we demonstrate that there is nonvanishing 3-torsion in (H) over bar (d)(M-n : Z) whenever v(n) <= d <= [n-6/2], where v(n) =[n-4/3]. By results due to Bouc and to Shareshian and Wachs, (H) over bar (d)(M-n : Z) is a nontrivial elementary 3-group for almost all n and the bottom nonvanishing homology group of M. for all n 0 2. Second, we prove that (H) over bar (d)(M-n : Z) is a nontrivial 3-group whenever v(n) <= d <= [2n-9/5]. Third, for each k >= 0, we show that there is a polynomial f(k)(r) of degree 3k such that the dimension of (H) over bar (k-1+r) (M2k+1+3r:Z(3)), viewed as a vector space over Z(3), is at most f(k)(r) for all r >= k + 2.

Place, publisher, year, edition, pages
2008. Vol. 115, no 8, p. 1504-1526
Keyword [en]
Matching complex, Simplicial homology, Long exact sequence, chessboard complexes
Identifiers
URN: urn:nbn:se:kth:diva-17919DOI: 10.1016/j.jcta.2008.03.001ISI: 000260441300011Scopus ID: 2-s2.0-52749092281OAI: oai:DiVA.org:kth-17919DiVA, id: diva2:335964
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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  • apa
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  • de-DE
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