### Abstract

We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homotopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group - a quotient of algebraic K-theory of the integral group ring of the fundamental group - and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.

Original language | English (US) |
---|---|

Pages (from-to) | 739-759 |

Number of pages | 21 |

Journal | Nuclear Physics B |

Volume | 853 |

Issue number | 3 |

DOIs | |

State | Published - Dec 21 2011 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics