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Topology/Geometry Seminar
Thursday, November 13, 2008
4:00 pm,
210 LRC
Stacy Hoehn
University of Notre Dame
Parametrized Wall Finiteness and Siebenmann End Obstructions.
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.
We meet weekly on Thursday afternoons, alternating between Penn State Altoona and Penn State University Park. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Fall 2008 semester: Wojtek Dorabiala and Aissa Wade.
