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arXiv · 0706.3973

Whitehead-Torsion und Faserungen

Wolfgang Steimle
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Abstract

This work treats on the question whether a given map f: M -> B of smooth closed manifolds is homotopic to a smooth fiber bundle. We define a first obstruction in H^1(B;Wh(π_1(E))) and, provided that this obstruction vanishes and one additional condition is verified, a second obstruction in Wh(π_1(E)) >. Both elements vanish if the answer to the above question is positive. In the case where B is the 1-sphere and the dimension of M exceeds five, we show that the converse is also true, using a relationship with two obstructions defined by Farrell in this particular situation.

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Wolfgang Steimle. 2007-06-27. Whitehead-Torsion und Faserungen. https://arxiv.org/abs/0706.3973

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