A new approach to quantize the gavitational field is presented. It is based on the observation that the quantum character of matter becomes more significant as one gets closer to the big bang. As the metric loses its meaning, it makes sense to consider Schrödinger's three generic types of manifolds — unconnected differentiable, affinely connected, and metrically connected — as a temporal sequence following the big bang. Hence one should quantize the gravitational field on general differentiable manifolds or on affinely connected manifolds. The SL(2,C) gauge theory of gravitation is employed to explore this possibility. Within this framework, the quantization itself may well be canonical.