Connectivity of h-complexes

Patricia Hersh

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Connectivity of h-complexes

Patricia Hersh

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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.

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Patricia Hersh. 2003-11-16. Connectivity of h-complexes. https://arxiv.org/abs/math/0311271

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