The fundamental group of the Quillen complex of the symmetric group

[摘要] In this paper, we investigate the fundamental group of the Quillen complex of the symmetric group DeltaAp (S-n). We show that when p is an odd prime the simplicial complex DeltaAp (S-n) is simply connected if and only if 3p + 2 less than or equal to n < p(2) or n greater than or equal to p(2) + p. Furthermore, we determine the fundamental group pi(1) (A(P)(SO) in all cases except those where p greater than or equal to 5 and n is an element of {3p, 3p + 1} andtbatwhere p = 3 and n = 10. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-01

[关键词] subgroup complexes;Quillen complex;symmetric group;fundamental group;simple connectivity