Simple Connectivity of the Quillen Complex of GLn(q) Original Research Article

The structure of the Quillen complex of GLn(q) at p, denoted imagep(GLn(q)), is known when p is the characteristic prime, and when pq − 1. In particular, in these cases, it is known that imagep(GLn(q)) is simply connected whenever mp(GLn(q)) ≥ 3. In this paper it is shown that mp(GLn(q)) ≥ 3 implies imagep(GLn(q)) is simply connected for all primes.