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The actions, anomalies, and quantization conditions allow the M2-brane andthe M5-brane to support, in a natural way, structures beyond Spin on theirworldvolumes. The main examples are twisted String structures. This alsoextends to twisted String^c structures, which we introduce and relate totwisted String structures. The relation of the C-field to Chern-Simons theorysuggests the use of the String cobordism category to describe the M2-brane.

Geometric and topological structures related to M-branes II: Twisted String and String^c structures