Cohen-Macaulay cell complexes

Details Cohen-Macaulay cell complexes Cohen-Macaulay cell complexes

2005-02-25

arxiv.org/abs/math/0502541v4

Algebraic and geometric combinatorics, p.205-220, Contemp. Math. 423, Amer. Math. Soc., Providence, RI, 2006

Mathematics

Combinatorics

15 pages. Added references

Scientific paper

We show that a finite regular cell complex with the intersection property is a Cohen-Macaulay space iff the top enriched cohomology module is the only nonvanishing one. We prove a comprehensive generalization of Balinski's theorem on convex polytopes. Also we show that for any Cohen-Macaulay cell complex as above, although there is no generalization of the Stanley-Reisner ring of simplicial complexes, there is a generalization of its canonical module.

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