Homotopy coherent diagrams and approximate fibrations

Wolfgang Steimle

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arXiv · 1107.5213

Homotopy coherent diagrams and approximate fibrations

Wolfgang Steimle

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Abstract

Let p be a fibration over a finite simplicial complex, whose fibers have the homotopy type of finite simplicial complexes. Then p is equivalent to an approximate fibration whose total space is a compact ENR. The proof uses homotopy coherent diagrams and their homotopy colimits. We also comment on the simple homotopy type of the total space and give an application to the fibering of Hilbert cube manifolds.

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Wolfgang Steimle. 2011-09-28. Homotopy coherent diagrams and approximate fibrations. https://arxiv.org/abs/1107.5213

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