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Order complexes of coset posets of finite groups are not contractible

Article ID Journal Published Year Pages File Type
4665154 Advances in Mathematics 2016 16 Pages PDF
Abstract

We show that the order complex of the poset of all cosets of all proper subgroups of a finite group G   is never F2F2-acyclic and therefore never contractible. This settles a question of K.S. Brown.

Keywords
Order complexFinite group
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
Preview
Order complexes of coset posets of finite groups are not contractible
Authors
John Shareshian, Russ Woodroofe,
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Journal
Advances in Mathematics
Journal: Advances in Mathematics
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