Geometry & Topology

Obstructions to stably fibering manifolds

Wolfgang Steimle

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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.

Article information

Geom. Topol., Volume 16, Number 3 (2012), 1691-1724.

Received: 26 July 2011
Accepted: 23 May 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 19J10: Whitehead (and related) torsion 55R10: Fiber bundles
Secondary: 57N20: Topology of infinite-dimensional manifolds [See also 58Bxx]

fibering a manifold algebraic $K$–theory of spaces


Steimle, Wolfgang. Obstructions to stably fibering manifolds. Geom. Topol. 16 (2012), no. 3, 1691--1724. doi:10.2140/gt.2012.16.1691.

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