Geometry & Topology

Obstructions to stably fibering manifolds

Wolfgang Steimle

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732446

Digital Object Identifier
doi:10.2140/gt.2012.16.1691

Mathematical Reviews number (MathSciNet)
MR2967061

Zentralblatt MATH identifier
1251.19003

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

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

Citation

Steimle, Wolfgang. Obstructions to stably fibering manifolds. Geom. Topol. 16 (2012), no. 3, 1691--1724. doi:10.2140/gt.2012.16.1691. https://projecteuclid.org/euclid.gt/1513732446


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