The gluing problem in the fusion systems of the symmetric, alternating and linear groups

A solution to Linckelmannʼs gluing problem in all fusion systems of blocks yields an alternative formulation of Alperinʼs weight conjecture. Using Bredon equivariant cohomology techniques we solve the gluing problem in fusion systems (of blocks) which are isomorphic to the fusion systems of the symmetric groups or the alternating groups or GLd(q) or SLd(q) at the defining characteristic.