Given a fusion system F on a finite p-group P, where p is a prime, we show that the partially ordered set of isomorphism classes in F of chains of non-trivial subgroups of P, considered as topological space, is contractible, further generalising Symonds’ proof [19] of a conjecture of Webb [23, 24] and its generalisation to non-trivial Brauer pairs associated with a p-block by Barker [1]
