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Betti numbers of skeletons
Roksvold, Jan...

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Betti numbers of skeletons by Roksvold, Jan ( Author )
Lemonjar Open Access
N.A
01-01-2015
We demonstrate that the Betti numbers associated to an N-graded minimal free resolution of the Stanley-Reisner ring of the (d-1)-skeleton of a simplicial complex of dimension d can be expressed as a Z-linear combination of the corresponding Betti numbers of the complex itself. An immediate implication of our main result is that the projective dimension of the Stanley-Reisner ring of the (d-1)-skeleton is at most one greater than the projective dimension of the Stanley-Reisner ring of the original complex, and it thus provides a new and direct proof of this. Our result extends immediately to matroids and their truncations. A similar result for matroid elongations can not be hoped for, but we do obtain a weaker result for these.
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Article
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36.88 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.05670
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