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- Jonsson, Jakob
(författare)
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More Torsion in the Homology of the Matching Complex
- 2010
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Ingår i: Experimental Mathematics. - : Informa UK Limited. - 1058-6458 .- 1944-950X. ; 19:3, s. 363-383
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Tidskriftsartikel (refereegranskat)abstract
- A matching on a set X is a collection of pairwise disjoint subsets of X of size two Using computers, we analyze the integral homology of the matching complex M, which is the simplicial complex of matchings on the set {1, ,n} The main result is the detection of elements of order p in the homology for p is an element of {5, 7, 11, 13} Specifically, we show that there are elements of order 5 in the homology of M-n for n >= 18 and for n is an element of {14, 16} The only previously known value was n = 14, and in this particular case we have a new computer-free proof Moreover, we show that there are elements of order 7 in the homology of M-n for all odd a between 23 and 41 and for n = 30 In addition, there are elements of order 11 in the homology of M-47 and elements of order 13 in the homology of M-62 Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of (H) over tilde (d)(M-n, Z) for 13 <= n <= 16, a complete description of the homology already exists for n <= 12 To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of M-n obtained by letting certain groups act on the chain complex.
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