Obstructions to stably fibering manifolds

Steimle, Wolfgang¹

¹ Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany

Geometry & topology, Tome 16 (2012) no. 3, pp. 1691-1724.

Résumé

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.

Détail

DOI : 10.2140/gt.2012.16.1691

Classification : 19J10, 55R10, 57N20
Keywords: fibering a manifold, algebraic $K$–theory of spaces

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