Skip to main content

Approximate fibrations-a geometric perspective

Part of the Lecture Notes in Mathematics book series (LNM,volume 870)

Keywords

  • Lift Property
  • Hilbert Cube
  • High Dimensional Manifold
  • Topology Proceeding
  • Point Inverse

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • G. Allaud and E. Fadell, A fiber homotopy extension theorem, Trans. Amer. Math. Soc., 104(1962), 239–251.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • S. Armentrout, Cellular decomposition of 3-manifolds that yeild 3-manifolds, Memoirs Amer. Math. Soc., 107(1971).

    Google Scholar 

  • S. Armentrout and T. M. Price, Decompositions into compact sets with UV-properties, Trans. Amer. Math. Soc., 141(1969), 433–442.

    MathSciNet  MATH  Google Scholar 

  • R. H. Bing, The Kline sphere characterization problem, Bull. Amer. Math. Soc., 52(1946) 644–653.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • K. Borsuk, Theory of Retracts, Polish Scientific Publishers, Warsaw, 1967.

    MATH  Google Scholar 

  • B2 K. Borsuk, Theory of Shape, Lecture Notes Series NO. 28, Matematisk Inst. Aarhaus. Univ, 1971.

    Google Scholar 

  • C1 T. A. Chapman, Lectures on Hilbert Cube Manifolds, C. B. M. S. Regional Conference Series in Math., No. 28, 1976.

    Google Scholar 

  • C2 T. A. Chapman, Approximating maps into fiber bundles by homeomorphisms, Rocky Mt. J. of Math. 10(1980), 333–350.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C3 T. A. Chapman, Carving up manifolds into block bundles. Preliminary Version.

    Google Scholar 

  • T. Chapman and S. Ferry, Hurewicz fiber maps with ANR fibers, Topology 16 (1977), 131–143.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C-D1 D. Coram and P. Duvall, Approximate fibrations, Rocky Mt. J. of Math. 7(1977), 275–288.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C-D2 D. Coram and P. Duvall, Approximate fibrations and a movability condition for maps., Pac. J. of Math, 72(1977), 41–56.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C-D3 D. S. Coram and P. F. Duvall, Jr., Mappings from S3 to S2 whose point inverses have the shape of a circle., Gen. Top. and Appl., 19(1979), 239–246.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C-D4 D. S. Coram and P. F. Duvall, Jr., Non-degenerate k-sphere mappings, Topology Proceedings, Vol. 4, 1979.

    Google Scholar 

  • C-D5 D. Coram and P. Duvall, A Hurewicz-type theorem for approximate fibrations, Proc. Amer. Math. Soc. 78(1980), 443–448.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C-D6 D. S. Coram and P. F. Duvall, Finiteness theorems for approximate fibrations, preprint.

    Google Scholar 

  • C-D7 D. S. Coram and P. F. Duvall, Local n-connectivity and approximate lifting, preprint.

    Google Scholar 

  • D. S. Coram, Decompositions of S3 into circles, talk given at Austin Topology Summer Conference, preprint.

    Google Scholar 

  • J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.

    MATH  Google Scholar 

  • D-H1 P. F. Duvall, Jr. and L. S. Husch, Fundamental dimension of fibers of approximate fibrations, Topology Proceedings, Vol. 3 (1978).

    Google Scholar 

  • D-H2 P. F. Duvall, Jr. and L. S. Husch, Fundamental dimension and suspension of approximate fibrations, Proc. Amer. Math. Soc. 79(1980), 122–126.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • E. Fadell, On fiber spaces, Trans. Amer. Math. Soc. 90(1959), 1–14.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Fe1 S. Ferry, Approximate fibrations with non-finite fibers, Proc. Amer. Math. Soc. 64(1977), 335–345.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Fe2 S. Ferry, Strongly regular mappings with compact ANR fibers are Hurewicz fibrings, Poc. J. Math. 75(1978), 373–382.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • R. Geoghogan (ed.) Open problems in infinite dimensional topology, Topology Proceedings, Vol. 4, 1979, 287–338.

    Google Scholar 

  • G1 R. E. Goad, Local homotopy properties of maps and approximation by fiber bundle projection, Thesis Univ. of Ga. (1976).

    Google Scholar 

  • G2 R. E. Goad, Approximate torus fibrations of high dimensional manifolds can be approximated by torus bundle projections, preprint.

    Google Scholar 

  • S. T. Hu, Theory of Retracts, Wayne State University Press, Detroit, 1965.

    MATH  Google Scholar 

  • H1 L. Husch, Approximating approximate fibrations by fibrations, Can. J. Math. 29(1977), 897–913.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • H2 L. Husch, Fibres of Hurewicz and approximate fibrations, Math. Scand. 43(1978), 44–48.

    MathSciNet  MATH  Google Scholar 

  • L. S. Husch and T. M. Price, Finding a boundary for a 3-manifold, Ann. Math. 91(1970), 223–235.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • K1 G. Kozlowski, Factorization of certain maps up to homotopy, Proc. Amer. Math. Soc. 21(1969), 88–92.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • K2 G. Kozlowski, Images of ANR's, Trans. Amer. Math. Soc., (to appear).

    Google Scholar 

  • L1 R. C. Lacher, Cell-like mappings I, Pac. J. of Math. 30(1969), 717–731.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • L2 R. C. Lacher, Cellularity criteria for maps, Mich. Math. Jour. 17(1970), 385–396.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • L3 R. C. Lacher, Finiteness theorems in the study of mappings between manifolds, Proc. of the Univ. of Okla. Topo. Conf. (1972), 79–96.

    Google Scholar 

  • L4 R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83(1977), 495–552.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • S. D. Liao, Some theorems on the dimension of fiber spaces, Amer. J. Math. 71(1949), 231–240.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • M1 S. Mardešić, Strongly movable compacta and shape retracts, Proc. Intern. Sym. on Top. and its Appl. (Budva, 1972), 163–166.

    Google Scholar 

  • M2 S. Mardešić, Shapes for topological spaces, Cen. Top. and Appl. 3(1973), 265–282.

    MathSciNet  MATH  Google Scholar 

  • L. McAuley, Proceedings of the Conf. on Monotone mappings and open mappings, State Univ. of N. Y. at Binghamton, 1970.

    Google Scholar 

  • R. L. Moore, Concerning upper semicontinuous collections of continua, Trans. Amer. Math. Soc. 27(1925), 416–428.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • S. Nowak, On the fundamental dimension of approximately 1-connected compacta, Fund. Math. 89(1975), 61–79.

    MathSciNet  MATH  Google Scholar 

  • Frank Quinn, Ends of maps and applications, Ann. of Math. 119(1979), 275–331.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • L. C. Siebenmann, Approximating cellular maps with homeomorphisms, Topology, 11(1972), 271–294.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • E. H. Spanier, Algebraic Topology, McGraw-Hill Book Co., New York (1966).

    MATH  Google Scholar 

  • G. Unger, Conditions for a mapping to have the slicing structure property, Pac. J. of Math., 30(1969), 549–553.

    CrossRef  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Coram, D.S. (1981). Approximate fibrations-a geometric perspective. In: Mardešić, S., Segal, J. (eds) Shape Theory and Geometric Topology. Lecture Notes in Mathematics, vol 870. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089706

Download citation

  • DOI: https://doi.org/10.1007/BFb0089706

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10846-7

  • Online ISBN: 978-3-540-38749-7

  • eBook Packages: Springer Book Archive