Abstract
By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on (4r − 1)-dimensional manifolds with no assumption that the 3rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on (4r − 1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on (4r − 1)-dimensional manifolds and the Han–Yu rigidity theorem to the (a, b) case.
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