### Abstract

The M-theory field strength and its dual, given by the integral lift of the left-hand side of the equation of motion, both satisfy certain cohomological properties. We study the combined fields and observe that the multiplicative structure on the product of the corresponding degree four and degree eight cohomology fits into that given by Spin K-theory. This explains some earlier results and leads naturally to the use of Spin characteristic classes. We reinterpret the one-loop term in terms of such classes and we show that it is a homotopy invariant. We argue that the various anomalies have natural interpretations within Spin K-theory. In the process, mod 3 reductions play a special role.

Original language | English (US) |
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Pages (from-to) | 387-401 |

Number of pages | 15 |

Journal | Journal of Geometry and Physics |

Volume | 58 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2008 |

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### Keywords

- Characteristic classes
- K-theory and generalized cohomology
- Spin bundles
- Topological anomalies in M-theory

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology