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In this talk I discuss the use of bordism theory in the analysis of type IIB string theory. After an introduction of the role of bordism groups in the analysis of anomalies and the consistency of quantum gravity, I will discuss the relevant groups for type IIB string theory including duality transformations. This leads to two surprising results. First, the duality of type IIB, as we know it, is anomalous. Second, for a consistent quantum gravity we need to include new defects and backgrounds, with the potential for interesting applications.