Quillen's conjecture for the p-subgroup complex is known to hold for solvable and p-solvable groups since the work of Quillen, Aschbacher, Smith and Alperin in the 80's and 90's. Here we present a new geometric approach to the subject. This includes an asymptotic version for the p-solvable case that does not use the Classification of the Finite Simple Groups. The methods are potentially applicable to the general case of the conjecture.