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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Obstructions to stably fibering manifolds

Wolfgang Steimle

Geometry & Topology 16 (2012) 1691–1724
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