This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
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.
S. Armentrout, Cellular decomposition of 3-manifolds that yeild 3-manifolds, Memoirs Amer. Math. Soc., 107(1971).
S. Armentrout and T. M. Price, Decompositions into compact sets with UV-properties, Trans. Amer. Math. Soc., 141(1969), 433–442.
R. H. Bing, The Kline sphere characterization problem, Bull. Amer. Math. Soc., 52(1946) 644–653.
K. Borsuk, Theory of Retracts, Polish Scientific Publishers, Warsaw, 1967.
B2 K. Borsuk, Theory of Shape, Lecture Notes Series NO. 28, Matematisk Inst. Aarhaus. Univ, 1971.
C1 T. A. Chapman, Lectures on Hilbert Cube Manifolds, C. B. M. S. Regional Conference Series in Math., No. 28, 1976.
C2 T. A. Chapman, Approximating maps into fiber bundles by homeomorphisms, Rocky Mt. J. of Math. 10(1980), 333–350.
C3 T. A. Chapman, Carving up manifolds into block bundles. Preliminary Version.
T. Chapman and S. Ferry, Hurewicz fiber maps with ANR fibers, Topology 16 (1977), 131–143.
C-D1 D. Coram and P. Duvall, Approximate fibrations, Rocky Mt. J. of Math. 7(1977), 275–288.
C-D2 D. Coram and P. Duvall, Approximate fibrations and a movability condition for maps., Pac. J. of Math, 72(1977), 41–56.
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.
C-D4 D. S. Coram and P. F. Duvall, Jr., Non-degenerate k-sphere mappings, Topology Proceedings, Vol. 4, 1979.
C-D5 D. Coram and P. Duvall, A Hurewicz-type theorem for approximate fibrations, Proc. Amer. Math. Soc. 78(1980), 443–448.
C-D6 D. S. Coram and P. F. Duvall, Finiteness theorems for approximate fibrations, preprint.
C-D7 D. S. Coram and P. F. Duvall, Local n-connectivity and approximate lifting, preprint.
D. S. Coram, Decompositions of S3 into circles, talk given at Austin Topology Summer Conference, preprint.
J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
D-H1 P. F. Duvall, Jr. and L. S. Husch, Fundamental dimension of fibers of approximate fibrations, Topology Proceedings, Vol. 3 (1978).
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.
E. Fadell, On fiber spaces, Trans. Amer. Math. Soc. 90(1959), 1–14.
Fe1 S. Ferry, Approximate fibrations with non-finite fibers, Proc. Amer. Math. Soc. 64(1977), 335–345.
Fe2 S. Ferry, Strongly regular mappings with compact ANR fibers are Hurewicz fibrings, Poc. J. Math. 75(1978), 373–382.
R. Geoghogan (ed.) Open problems in infinite dimensional topology, Topology Proceedings, Vol. 4, 1979, 287–338.
G1 R. E. Goad, Local homotopy properties of maps and approximation by fiber bundle projection, Thesis Univ. of Ga. (1976).
G2 R. E. Goad, Approximate torus fibrations of high dimensional manifolds can be approximated by torus bundle projections, preprint.
S. T. Hu, Theory of Retracts, Wayne State University Press, Detroit, 1965.
H1 L. Husch, Approximating approximate fibrations by fibrations, Can. J. Math. 29(1977), 897–913.
H2 L. Husch, Fibres of Hurewicz and approximate fibrations, Math. Scand. 43(1978), 44–48.
L. S. Husch and T. M. Price, Finding a boundary for a 3-manifold, Ann. Math. 91(1970), 223–235.
K1 G. Kozlowski, Factorization of certain maps up to homotopy, Proc. Amer. Math. Soc. 21(1969), 88–92.
K2 G. Kozlowski, Images of ANR's, Trans. Amer. Math. Soc., (to appear).
L1 R. C. Lacher, Cell-like mappings I, Pac. J. of Math. 30(1969), 717–731.
L2 R. C. Lacher, Cellularity criteria for maps, Mich. Math. Jour. 17(1970), 385–396.
L3 R. C. Lacher, Finiteness theorems in the study of mappings between manifolds, Proc. of the Univ. of Okla. Topo. Conf. (1972), 79–96.
L4 R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83(1977), 495–552.
S. D. Liao, Some theorems on the dimension of fiber spaces, Amer. J. Math. 71(1949), 231–240.
M1 S. Mardešić, Strongly movable compacta and shape retracts, Proc. Intern. Sym. on Top. and its Appl. (Budva, 1972), 163–166.
M2 S. Mardešić, Shapes for topological spaces, Cen. Top. and Appl. 3(1973), 265–282.
L. McAuley, Proceedings of the Conf. on Monotone mappings and open mappings, State Univ. of N. Y. at Binghamton, 1970.
R. L. Moore, Concerning upper semicontinuous collections of continua, Trans. Amer. Math. Soc. 27(1925), 416–428.
S. Nowak, On the fundamental dimension of approximately 1-connected compacta, Fund. Math. 89(1975), 61–79.
Frank Quinn, Ends of maps and applications, Ann. of Math. 119(1979), 275–331.
L. C. Siebenmann, Approximating cellular maps with homeomorphisms, Topology, 11(1972), 271–294.
E. H. Spanier, Algebraic Topology, McGraw-Hill Book Co., New York (1966).
G. Unger, Conditions for a mapping to have the slicing structure property, Pac. J. of Math., 30(1969), 549–553.
Editor information
Rights 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