Homology of generalized partition posets

Details Homology of generalized partition posets Homology of generalized partition posets

2004-05-16

arxiv.org/abs/math/0405312v3

J. Pure Appl. Algebra 208 (2007), no. 2, 699-725

Mathematics

Algebraic Topology

Final version. To appear in JPAA

Scientific paper

10.1016/j.jpaa.2006.03.012

We define a poset of partitions associated to an operad. We prove that the
operad is Koszul if and only if the poset is Cohen-Macaulay.
In one hand, this characterisation allows us to compute the homology of the
poset. This homology is given by the Koszul dual operad. On the other hand, we
get new methods for proving that an operad is Koszul.

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