Connectivity of h-complexes

Authors:
Patricia Hersh
Affiliations:
Department of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor,MI
Venue:
Journal of Combinatorial Theory Series A
Year:
2004

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Abstract

This paper verifies a conjecture of Edelman and Reiner regarding the homology of the h-complex of a Boolean algebra. A discrete Morse function with no low-dimensional critical cells is constructed, implying a lower bound on connectivity. This together with an Alexander duality result of Edelman and Reiner implies homology vanishing also in high dimensions. Finally, possible generalizations to certain classes of supersolvable lattices are suggested.