### Abstract

The structure space S(m) of a closed topological m-manifold M classifies bundles whose fibers are closed m-manifolds equipped with a homotopy equivalence to M. We construct a highly connected map from S(M) to a concoction of algebraic L-theory and algebraic K-theory spaces associated with M. The construction refines the well known surgery theoretic analysis of the block structure space of M in terms of L-theory.

Original language | English |
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Place of Publication | Rhode Island |

Publisher | American Mathematical Society |

Number of pages | 110 |

ISBN (Electronic) | 9781470417208 |

ISBN (Print) | 9781470409814 |

DOIs | |

Publication status | Published - 1 Sep 2014 |

### Publication series

Name | Memoirs of the American Mathematical Society |
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Publisher | American Mathematical Society |

No. | 1084 |

Volume | 231 |

ISSN (Print) | 0065-9266 |

ISSN (Electronic) | 1947-6221 |

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## Cite this

Weiss, M., & Williams, B. E. (2014).

*Automorphisms of Manifolds and Algebraic K-Theory: Part III*. (Memoirs of the American Mathematical Society; Vol. 231, No. 1084). American Mathematical Society. https://doi.org/10.1090/memo/1084