Finiteness theorems for approximate fibrations

Authors:
D. S. Coram and P. F. Duvall

Journal:
Trans. Amer. Math. Soc. **269** (1982), 383-394

MSC:
Primary 55R65; Secondary 55P55, 57N55

MathSciNet review:
637696

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Abstract: This paper concerns conditions on the point inverses of a mapping between manifolds which insure that it is an approximate fibration almost everywhere. The primary condition is -movability, which says roughly that nearby point inverses include isomorphically on the th shape group into a mutual neighborhood. Suppose is a mapping which is -movable for , and . An earlier paper proved that is an approximate fibration when . If instead , this paper proves that there is a locally finite set such that is an approximate fibration. Also if and all of the point inverses are FANR's with the same shape, then there is a locally finite set such that is an approximate fibration.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0637696-9

Keywords:
Approximate fibration,
movability,
mapping between manifolds

Article copyright:
© Copyright 1982
American Mathematical Society