The University of Michigan Combinatorics Seminar
Winter 2002
January 18, 4:10-5:00, 3866 East Hall





Hodge structure for posets

Phil Hanlon

University of Michigan




Abstract

We define the notion of a Hodge structure for a poset P, which is an action of Sr+1 on the r-chains of P, for all r. These actions must satisfy a certain condition relative to the usual boundary map on r-chains. We show that under this condition, the homology of P admits the same kind of Hodge decomposition as does the Hochschild homology of a commutative algebra. As a specific example, we consider the poset of subsets of [nk] which have cardinality divisible by k.