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Author Jonsson, Jakob
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Matching Complex ♦ Exact Sequence ♦ Nontrivial 3-group Whenever ♦ Different Way ♦ Complete Graph Kn ♦ Reduced Simplicial Homology ♦ Nontrivial Ele-mentary 3-group ♦ Long Exact Sequence ♦ Polynomial Fk ♦ 3-torsion Part ♦ Vector Space ♦ Bottom Nonvanishing Homology Group ♦ Simplicial Complex ♦ Several Result ♦ Com-plex Mn
Abstract 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 com-plex Mn, which is the simplicial complex of matchings in the complete graph Kn. Combining these sequences in different ways, we prove several results about the 3-torsion part of the homology of Mn. First, we demonstrate that there is nonva-nishing 3-torsion in H̃d(Mn;Z) whenever νn ≤ d ≤ bn−62 c, where νn = dn−43 e. By results due to Bouc and to Shareshian and Wachs, H̃νn(Mn;Z) is a nontrivial ele-mentary 3-group for almost all n and the bottom nonvanishing homology group of Mn for all n 6 = 2. Second, we prove that H̃d(Mn;Z) is a nontrivial 3-group whenever νn ≤ d ≤ b2n−95 c. Third, for each k ≥ 0, we show that there is a polynomial fk(r) of degree 3k such that the dimension of H̃k−1+r(M2k+1+3r;Z3), viewed as a vector space over Z3, is at most fk(r) for all r ≥ k + 2.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Publisher Date 2008-01-01