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arXiv:1406.6067 [math.CO]AbstractReferencesReviewsResources

Order complexes of coset posets of finite groups are not contractible

John Shareshian, Russ Woodroofe

Published 2014-06-23, updated 2014-07-29Version 2

We show that the order complex of the poset of all cosets of all proper subgroups of a finite group $G$ is never $\mathbb{F}_{2}$-acyclic and therefore never contractible. This settles a question of K. S. Brown.

Comments: 16 pages. v2 fixes minor errors
Categories: math.CO, math.GR
Subjects: 05E45, 20E99, 06B30
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