Volume 16, issue 3 (2012)

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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