The tragedy has several turning points, but the major one is when Oedipus murders a stranger on the highway. He doesn't realize that the stranger is his father. Oedupus then marries the wife of the man he killed, not realizing that she is his mother. Another major turning point is when Oedipus insists on sending a messenger to find out from a wise prophet who his parents are. When he learns that he has murdered hois own father and married his own mother, he gouges out his eyes and calls down a curse on himself. That is also a turning point.
Since everything that happens to Oedipus and everything he does comes about because of a curse leveled against his family, everything is fated. It's all destined to happen and in that sense there is no turning point. There's no way to escape the curse and everything unfolds as predicted.
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