Approximate fibrations with nonfinite fibers
HTML articles powered by AMS MathViewer
- by Steve Ferry PDF
- Proc. Amer. Math. Soc. 64 (1977), 335-345 Request permission
Abstract:
It is shown that every ANR fibration over ${S^1}$ 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.References
- R. D. Anderson and T. A. Chapman, Extending homeomorphisms to Hilbert cube manifolds, Pacific J. Math. 38 (1971), 281–293. MR 319204
- K. Borsuk, Theory of shape, Lecture Notes Series, No. 28, Aarhus Universitet, Matematisk Institut, Aarhus, 1971. MR 0293602
- T. A. Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Mathematics, No. 28, American Mathematical Society, Providence, R.I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975. MR 0423357 T. A. Chapman and S. Ferry, Obstruction to finiteness in the proper category (preprint). —, Hurewicz fiberings with ANR fibers, Topology (to appear).
- Marshall M. Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics, Vol. 10, Springer-Verlag, New York-Berlin, 1973. MR 0362320 D. S. Coram and P. F. Duvall, Approximate fibrations (preprint). —, Approximate fibrations and a movability condition for maps (preprint).
- 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 375330, DOI 10.2307/1970939
- 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 R. E. Goad, Local homotopy properties of maps and approximation by fiber bundle projection, Thesis, Univ. of Georgia, 1976.
- L. S. Husch, Approximating approximate fibrations by fibrations, Canadian J. Math. 29 (1977), no. 5, 897–913. MR 500990, DOI 10.4153/CJM-1977-091-2
- R. C. Lacher, Cell-like mappings. I, Pacific J. Math. 30 (1969), 717–731. MR 251714 L. Mand, A generalization of cell-like mappings, Thesis, Univ. of Kentucky, 1975.
- 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 362324 J. E. West, Mapping Hilbert cube manifolds to ANR’s, Ann. of Math. (to appear).
- James E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), no. 2, 111–125. MR 288788
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 335-345
- MSC: Primary 55F65
- DOI: https://doi.org/10.1090/S0002-9939-1977-0461505-8
- MathSciNet review: 0461505