Approximate fibrations with nonfinite fibers

Author:
Steve Ferry

Journal:
Proc. Amer. Math. Soc. **64** (1977), 335-345

MSC:
Primary 55F65

MathSciNet review:
0461505

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every ANR fibration over with finitely dominated fiber is homotopy equivalent to an approximate fibration with compact ANR total space. This yields examples of approximate fibrations with arbitrary compact pointed FANR fibers.

**[A-Ch]**R. D. Anderson and T. A. Chapman,*Extending homeomorphisms to Hilbert cube manifolds*, Pacific J. Math.**38**(1971), 281–293. MR**0319204****[B]**K. Borsuk,*Theory of shape*, Matematisk Institut, Aarhus Universitet, Aarhus, 1971. Lecture Notes Series, No. 28. MR**0293602****[Ch]**T. A. Chapman,*Lectures on Hilbert cube manifolds*, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR**0423357****[Ch-F]**T. A. Chapman and S. Ferry,*Obstruction to finiteness in the proper category*(preprint).**[Ch-F]**-,*Hurewicz fiberings with ANR fibers*, Topology (to appear).**[C]**Marshall M. Cohen,*A course in simple-homotopy theory*, Springer-Verlag, New York-Berlin, 1973. Graduate Texts in Mathematics, Vol. 10. MR**0362320****[C-D]**D. S. Coram and P. F. Duvall,*Approximate fibrations*(preprint).**[C-D]**-,*Approximate fibrations and a movability condition for maps*(preprint).**[E-G]**David A. Edwards and Ross Geoghegan,*Shapes of complexes, ends of manifolds, homotopy limits and the Wall obstruction*, Ann. of Math. (2)**101**(1975), 521–535. MR**0375330****[Fa]**F. Thomas Farrell,*The obstruction to fibering a manifold over a circle*, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 69–72. MR**0423376****[G]**R. E. Goad,*Local homotopy properties of maps and approximation by fiber bundle projection*, Thesis, Univ. of Georgia, 1976.**[H]**L. S. Husch,*Approximating approximate fibrations by fibrations*, Canad. J. Math.**29**(1977), no. 5, 897–913. MR**0500990****[L]**R. C. Lacher,*Cell-like mappings. I*, Pacific J. Math.**30**(1969), 717–731. MR**0251714****[M]**L. Mand,*A generalization of cell-like mappings*, Thesis, Univ. of Kentucky, 1975.**[S-G-H]**L. Siebenmann, L. Guillou, and H. Hähl,*Les voisinages ouverts réguliers: critères homotopiques d’existence*, Ann. Sci. École Norm. Sup. (4)**7**(1974), 431–461 (1975) (French). MR**0362324****[W]**J. E. West,*Mapping Hilbert cube manifolds to ANR's*, Ann. of Math. (to appear).**[W]**James E. West,*Mapping cylinders of Hilbert cube factors*, General Topology and Appl.**1**(1971), no. 2, 111–125. MR**0288788**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
55F65

Retrieve articles in all journals with MSC: 55F65

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0461505-8

Keywords:
Approximate fibration,
shape,
finiteness obstruction

Article copyright:
© Copyright 1977
American Mathematical Society