## Geometry & Topology

### Obstructions to stably fibering manifolds

Wolfgang Steimle

#### 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
Accepted: 23 May 2012
First available in Project Euclid: 20 December 2017

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

#### 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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