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Dehn fillings of Klein bottle bundles

Published online by Cambridge University Press:  24 October 2008

Wolfgang Heil  and
Pedja Raspopović
Wolfgang Heil
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306–3027, U.S.A.
Pedja Raspopović
Affiliation:
Department of Mathematics, University of Titograd, 81000 Titograd, Yugoslavia
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Extract

An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 255 - 270
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

[1]Baker, M.. Covers of Dehn fillings on once-punctured torus bundles. Preprint.Google Scholar
[2]Culler, M., Jaco, W., and Rubinstein, H.. Incompressible surfaces in once-punctured torus bundles. Proc. London Math. Soc. (3) 45 (1982), 385–419.CrossRefGoogle Scholar
[3]Floyd, W. and Hatcher, A.. Incompressible surfaces in punctured torus bundles. Topology Appl. 13 (1982), 263–282.CrossRefGoogle Scholar
[4]McGordon, C. and Luecke, J.. Knots are determined by their complements. Bull. Amer. Math. Soc. 20 (1989), 83–87.Google Scholar
[5]Hatcher, A. E.. On the boundary curves of incompressible surfaces. Pacific J. Math. 99 (1982), 373–377.CrossRefGoogle Scholar
[6]Hatcher, A. E.. Notes on basic 3-manifold topology. (Preprint).Google Scholar
[7]Hatcher, A. E. and Thurston, W.. Incompressible surfaces in 2-bridge knot complements. Invent. Math. 79 (1985), 225–246.CrossRefGoogle Scholar
[8]Heil, W.. On certain fiberings of M2 × S1. Proc. Amer. Math. Soc. 34 (1972), 280–286.Google Scholar
[9]Hempel, J.. 3-manifolds. Ann. of Math. Studies no. 86 (Princeton University Press, 1976).Google Scholar
[10]Jaco, W.. Lectures on 3-manifold topology. Regional Conf. Series in Math. no. 43 (1980).CrossRefGoogle Scholar
[11]Jaco, W.. Surfaces embedded in M2 × S1. Canad. J. Math. 22 (1970), 553–568.CrossRefGoogle Scholar
[12]Lickorish, W. B. R.. Homeomorphisms of non-orientable two-manifolds. Proc. Cambridge Philos. Soc. 59 (1963), 307–317.CrossRefGoogle Scholar
[13]Neumann, D. A.. 3-manifolds fibering over S1. Proc. Amer. Math. Soc. 58 (1976), 353–356.Google Scholar
[14]Orlik, P., Vogt, E. and Zieschang, H.. Zur Topologie gefaserter 3-dimensionaler Mannigfaltigkeiten. Topology 6 (1967), 49–64.CrossRefGoogle Scholar
[15]Raspopović, P.. Incompressible surfaces in punctured Klein bottle bundles. Preprint.Google Scholar
[16]Raspopović, P.. Incompressible surfaces in punctured Klein bottle bundles. Ph.D. thesis, Florida State University (1990).Google Scholar
[17]Scott, P.. The geometries of 3-manifolds. Bull. London Math. Soc. 15 (1983), 401–487.CrossRefGoogle Scholar
[18]Seifert, H.. Über die Topologie 3-dimensionaler gefaserter Räume. Ada Math. 60 (1933), 147–288. English translation inGoogle Scholar
A Textbook of Topology (Academic Press, 1980), pp. 358–422.Google Scholar
[19]Soma, T.. Equivariant surfaces in 3-manifolds with abelian group actions. Bull. Kyushu Inst. Tech. Math. Natur. Sci. 36 (1989), 1–9.Google Scholar
[20]Stallings, J.. On fibering certain 3 manifolds. In Topology of 3-Manifolds and Related Topics (Prentice Hall, 1962), pp. 95–100.Google Scholar
[21]Steenrod, N.. The Topology of Fibre Bundles (Princeton University Press, 1951).Google Scholar
[22]Thurston, W.. The Geometry and Topology of 3-manifolds. Lecture Notes, Princeton University (1979).Google Scholar
[23]Tollefson, J.. 3-manifolds fiberings over S1 with nonunique connected fiber. Proc. Amer. Math. Soc. 21 (1969), 79–80.Google Scholar
[24]Waldhausen, F.. Eine Klasse von 3-dimensionaler. Mannigfaltkeiten II. Invent. Math. 4 (1967), 87–117.CrossRefGoogle Scholar