  A new approach to quantize the gravitational 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 Schrodinger'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.
