Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T14:15:02.100Z Has data issue: false hasContentIssue false

The preimages of submanifolds

Published online by Cambridge University Press:  24 October 2008

Yongwu Rong
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan, U.S.A.
Shicheng Wang
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, P.R., China

Extract

All manifolds in this paper are piecewise linear (or smooth if one wishes).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Edmonds, A.. Deformation of maps to branched covering in dimension 2. Ann. of Math. 110 (1979), 113125.CrossRefGoogle Scholar
[2]Edmonds, A.. Deformation of maps to branched covering in dimension 3. Math. Ann. 245 (1979), 273279.CrossRefGoogle Scholar
[3]Epstein, D.. The degree of maps. Proc. London Math. Soc. 16 (1969), 369383.Google Scholar
[4]Haken, W.. On homotopy 3-sphere. Illinois J. Math. 10 (1966), 159180.CrossRefGoogle Scholar
[5]Hempel, J.. 3-manifolds. Ann of Math. Studies no. 86 (Princeton University Press, 1976).Google Scholar
[6]Hopf, . Zur Topologie der Abbidungen von Mannigfaltigkeiten, I, II. Math. Ann. 100 (1928), 579608Google Scholar
Hopf, . Zur Topologie der Abbidungen von Mannigfaltigkeiten, I, II. Math. Ann. 102 (1930), 562623.CrossRefGoogle Scholar
[7]Hudson, J.. Piecewise Linear Topology (Benjamin, 1969).Google Scholar
[8]Laudenbach, F.. Topologie de la Dimension Trots: Homotopie et Isotopie. Astérisque no. 12 (Société Mathématique de France, 1974).Google Scholar
[9]Lin, X.. On the root classes of mapping. Acta Math. Sinica (N.S.) 2 (1986), 199206.Google Scholar
[10]Luft, E. and Sjerve, D.. Degree 1 maps into lens spaces and free actions on homology spheres. Topology Appl. 37 (1990), 131136.CrossRefGoogle Scholar
[11]Kneser, H.. Glattung von Flächenabbildungen. Math. Ann. 100 (1928), 609658.CrossRefGoogle Scholar
[12]Rong, Y.. Degree one maps between geometric 3-manifolds. Trans. Amer. Math. Soc., to appear.Google Scholar
[13]Rong, Y.. Maps between Seifert fibered spaces of infinity π1. Preprint (1990).Google Scholar
[14]Rourke, C. and Sanderson, B. J.. Block bundle II, transversality. Ann. of Math. 87 (1968), 255277.Google Scholar
[15]Schirmer, H.. Mindestzahlen von Koinzidenzpunkt. J. Reine Angew. Math. 194 (1955), 2139.CrossRefGoogle Scholar
[16]Skora, R.. The degree of maps between surfaces. Math. Ann. 276 (1987), 415423.CrossRefGoogle Scholar
[17]Swarup, G. A.. On embedded spheres in 3-manifolds. Proc. Amer. Math. Soc. 19 (1969), 3144.Google Scholar
[18]Waldhausen, F.. On mappings of handlebodies and Heegaard splittings. In Topology of Manifolds (Markham Publishing Company, 1970), pp. 205211.Google Scholar