For more information about this meeting, contact Aissa Wade.

Title: | Parametrized Wall Finiteness and Siebenmann End Obstructions. |

Seminar: | Topology/Geometry Seminar |

Speaker: | Stacy Hoehn, University of Notre Dame |

Abstract: |

Given a finitely dominated space X, the classical finiteness obstruction of Wall is an element in a certain group that vanishes if and only if X is homotopy equivalent to a finite CW complex. Similarly, given a non-compact manifold M that satisfies certain tameness properties near its ends, the classical end obstruction of Siebenmann is an element in a certain group that vanishes if and only if M can be completed to a compact manifold with boundary.
Both of these classical obstructions have parametrized versions that answer questions about families of spaces. For example, the parametrized Wall obstruction of Dwyer-Weiss-Williams can be used to determine when a fibration whose fibers are finitely dominated is fiber homotopy equivalent to a fiber bundle whose fibers are compact manifolds. Meanwhile, a parametrized version of Siebenmann's end obstruction can be used to determine when a fiber bundle whose fibers are open manifolds with tame ends has a fiberwise completion to a fiber bundle whose fibers are compact manifolds with boundary. We will discuss the construction of both of these parametrized obstructions and their relationships to one another. |

### Room Reservation Information

Room Number: | 210 LRC, Altoonma |

Date: | 11 / 13 / 2008 |

Time: | 05:00pm - 06:00pm |