Obstructions to stably fibering manifolds

Steimle, Wolfgang

doi:10.2140/gt.2012.16.1691

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Obstructions to stably fibering manifolds

Wolfgang Steimle

Geometry & Topology 16 (2012) 1691–1724

DOI: 10.2140/gt.2012.16.1691

Abstract

Is a given map between compact topological manifolds homotopic to the projection map of a fiber bundle? In this paper obstructions to this question are introduced with values in higher algebraic $K$ –theory. Their vanishing implies that the given map fibers stably. The methods also provide results for the corresponding uniqueness question; moreover they apply to the fibering of Hilbert cube manifolds, generalizing results by Chapman and Ferry.

Keywords

fibering a manifold, algebraic $K$–theory of spaces

Mathematical Subject Classification 2010

Primary: 19J10, 55R10

Secondary: 57N20

References

Publication

Received: 26 July 2011

Accepted: 23 May 2012

Published: 3 August 2012

Proposed: Bill Dwyer

Seconded: Ronald J Stern, John Lott

Authors

Wolfgang Steimle
Mathematisches Institut Universität Bonn Endenicher Allee 60 D-53115 Bonn Germany
http://www.math.uni-bonn.de/people/steimle

Volume 16, issue 3 (2012)