dc.contributor.author | Ranicki, Andrew | |

dc.coverage.spatial | 20 | en |

dc.date.accessioned | 2003-11-18T10:25:36Z | |

dc.date.available | 2003-11-18T10:25:36Z | |

dc.date.issued | 2001-11-30 | |

dc.identifier.citation | http://arxiv.org/pdf/math.AT/0111316 | en |

dc.identifier.uri | http://hdl.handle.net/1842/243 | |

dc.description.abstract | The algebraic theory of surgery gives a necessary and suffcient chain level condition
for a space with n-dimensional Poincare duality to be homotopy equivalent to an n-
dimensional topological manifold. A relative version gives a necessary and suffcient
chain level condition for a simple homotopy equivalence of n-dimensional topological
manifolds to be homotopic to a homeomorphism. The chain level obstructions come
from a chain level interpretation of the fibre of the assembly map in surgery.
The assembly map A : Hn(X;L.) -> Ln(Z[Pi 1 | (X)]) is a natural transformation from
the generalized homology groups of a space X with coefficients in the 1-connective
simply-connected surgery spectrum L. to the non-simply-connected surgery obstruc-
tion groups L.(Z[Pi 1 | (X)]). The (Z;X)-category has objects based f.g. free Z-modules
with an X-local structure. The assembly maps A are induced by a functor from the
(Z;X)-category to the category of based f.g. free Z[Pi 1 | (X)]-modules. The generalized
homology groups H.(X;L.) are the cobordism groups of quadratic Poincare complexes
over (Z;X). The relative groups S.(X) in the algebraic surgery exact sequence of X
... -> Hn(X;L.)
A | en |

dc.format.extent | 204568 bytes | |

dc.format.mimetype | application/pdf | |

dc.language.iso | en | |

dc.publisher | Notes of lecture given at the Summer School on High-dimensional Manifold Topology, ICTP Trieste, May-June 2001. To appear in Vol. 1 of the Proceedings | en |

dc.subject | surgery exact sequence | en |

dc.subject | structure set | en |

dc.subject | total surgery obstruction | en |

dc.title | The structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstruction | en |

dc.type | Preprint | en |