Homotopy coherent diagrams and approximate fibrations

Details Homotopy coherent diagrams and approximate fibrations Homotopy coherent diagrams and approximate fibrations

2011-07-26

arxiv.org/abs/1107.5213v3

Mathematics

Algebraic Topology

25 pages. Corrected statement of 6.7 and 6.8

Scientific paper

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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