Whitehead-Torsion und Faserungen
Geometric Topology
2007-06-28 v1
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(\pi_1(E))) and, provided that this obstruction vanishes and one additional condition is verified, a second obstruction in Wh(\pi_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.
Keywords
Cite
@article{arxiv.0706.3973,
title = {Whitehead-Torsion und Faserungen},
author = {Wolfgang Steimle},
journal= {arXiv preprint arXiv:0706.3973},
year = {2007}
}